1. Az n! értékei, ahol 1 ≤ n ≤ 20 (MAPLE):

> x_n:=n!; seq(x_n,n=1..20);

1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800, 39916800, 479001600,

6227020800, 87178291200, 1307674368000, 20922789888000, 355687428096000,

6402373705728000, 121645100408832000, 2432902008176640000

2. Az (n alatt k) binomiális együtthatók értékei, ahol 0 ≤ k ≤ n ≤ 10 (MAPLE):

> seq([seq(binomial(n,k), k=0..n)], n=0..10);

[1], [1, 1], [1, 2, 1], [1, 3, 3, 1], [1, 4, 6, 4, 1], [1, 5, 10, 10, 5, 1],

[1, 6, 15, 20, 15, 6, 1], [1, 7, 21, 35, 35, 21, 7, 1],

[1, 8, 28, 56, 70, 56, 28, 8, 1], [1, 9, 36, 84, 126, 126, 84, 36, 9, 1],

[1, 10, 45, 120, 210, 252, 210, 120, 45, 10, 1]

3. Az n szám partíciói a tagok növekvő sorrendjében, ahol 0 ≤ n ≤ 8 (MAPLE):

>with(combinat):

> seq(partition(n), n=0..8);

[[]], [[1]], [[1, 1], [2]], [[1, 1, 1], [1, 2], [3]],

[[1, 1, 1, 1], [1, 1, 2], [2, 2], [1, 3], [4]],

[[1, 1, 1, 1, 1], [1, 1, 1, 2], [1, 2, 2], [1, 1, 3], [2, 3], [1, 4], [5]],

[[1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2], [1, 1, 2, 2], [2, 2, 2], [1, 1, 1, 3],

[1, 2, 3], [3, 3], [1, 1, 4], [2, 4], [1, 5], [6]],

[[1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 2], [1, 1, 1, 2, 2], [1, 2, 2, 2],

[1, 1, 1, 1, 3], [1, 1, 2, 3], [2, 2, 3], [1, 3, 3], [1, 1, 1, 4], [1, 2, 4],

[3, 4], [1, 1, 5], [2, 5], [1, 6], [7]],

[[1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1, 2], [1, 1, 1, 1, 2, 2],

[1, 1, 2, 2, 2], [2, 2, 2, 2], [1, 1, 1, 1, 1, 3], [1, 1, 1, 2, 3], [1, 2, 2, 3],

[1, 1, 3, 3], [2, 3, 3], [1, 1, 1, 1, 4], [1, 1, 2, 4], [2, 2, 4], [1, 3, 4],

[4, 4], [1, 1, 1, 5], [1, 2, 5], [3, 5], [1, 1, 6], [2, 6], [1, 7], [8]]

4. A p(n) partíciófüggvény értékei, ahol 0 ≤ n ≤ 20 (MAPLE):

> seq(numbpart(n), n=0..20);

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 101, 135, 176, 231, 297, 385, 490, 627

5. Az F_n Fibonacci-számok, ahol 0 ≤ n ≤ 30 (MAPLE):

> with(combinat, fibonacci): seq(fibonacci(n), n=0..30);

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181,

6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, 514229, 832040

6. Az L_n Lucas-számok, ahol 0 ≤ n ≤ 30 (MAPLE):

> with(combinat): L_n:=fibonacci(n+1)+fibonacci(n-1): # Lucas-szamok

> seq(L_n, n=0..30);

2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521, 843, 1364, 2207, 3571, 5778, 9349,

15127, 24476, 39603, 64079, 103682, 167761, 271443, 439204, 710647, 1149851, 1860498

7. A C_n Catalan-számok, ahol 0 ≤ n ≤ 30 (MAPLE):

> with(combinat): C_n:=(1/(n+1))*binomial(2*n,n): # Catalan-szamok

> seq(C_n, n=0..30);

1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, 742900, 2674440, 9694845,

35357670, 129644790, 477638700, 1767263190, 6564120420, 24466267020, 91482563640,

343059613650, 1289904147324, 4861946401452, 18367353072152, 69533550916004,

263747951750360, 1002242216651368, 3814986502092304

8. Az {n alatt k} = S(n,k) másodfajú Stirling-számok értékei, ahol 1 ≤ k ≤ n ≤ 10 (MAPLE):

> with(combinat): seq([seq(stirling2(n,k), k=1..n)], n=1..10);

[1], [1, 1], [1, 3, 1], [1, 7, 6, 1], [1, 15, 25, 10, 1], [1, 31, 90, 65, 15, 1],

[1, 63, 301, 350, 140, 21, 1], [1, 127, 966, 1701, 1050, 266, 28, 1],

[1, 255, 3025, 7770, 6951, 2646, 462, 36, 1],

[1, 511, 9330, 34105, 42525, 22827, 5880, 750, 45, 1]

9. A B(n) Bell-számok értékei, ahol 1 ≤ n ≤ 20 (MAPLE):

> with(combinat): seq(bell(n), n=1..20);

1, 2, 5, 15, 52, 203, 877, 4140, 21147, 115975, 678570, 4213597, 27644437, 190899322,

1382958545, 10480142147, 82864869804, 682076806159, 5832742205057, 51724158235372

10. Az [n alatt k] = s(n,k) elsőfajú Stirling-számok értékei, ahol 1 ≤ k ≤ n ≤ 10 (MAPLE):

> with(combinat): seq([(abs(stirling1(n,k)), k=1..n)], n=1..10);

[1], [1, 1], [2, 3, 1], [6, 11, 6, 1], [24, 50, 35, 10, 1],

[120, 274, 225, 85, 15, 1], [720, 1764, 1624, 735, 175, 21, 1],

[5040, 13068, 13132, 6769, 1960, 322, 28, 1],

[40320, 109584, 118124, 67284, 22449, 4536, 546, 36, 1],

[362880, 1026576, 1172700, 723680, 269325, 63273, 9450, 870, 45, 1]

11. A (-1)^{n-k} [n alatt k] = (-1)^{n-k} s(n,k) elsőfajú algebrai Stirling-számok értékei, ahol 1 ≤ k ≤ n ≤ 10 (MAPLE):

> with(combinat): seq([seq(stirling1(n,k), k=1..n)], n=1..10);

[1], [-1, 1], [2, -3, 1], [-6, 11, -6, 1], [24, -50, 35, -10, 1],

[-120, 274, -225, 85, -15, 1], [720, -1764, 1624, -735, 175, -21, 1],

[-5040, 13068, -13132, 6769, -1960, 322, -28, 1],

[40320, -109584, 118124, -67284, 22449, -4536, 546, -36, 1],

[-362880, 1026576, -1172700, 723680, -269325, 63273, -9450, 870, -45, 1]