A111886 Sixth column of triangle A112492 (inverse scaled Pochhammer symbols).

1, 1764, 1942416, 1744835904, 1413470290176, 1083688832185344, 806595068762689536, 590914962115587293184, 429295503918929370218496, 310518802877016005311463424, 224098118280955193084850733056

Offset

0,2

Comments

Also continuation of family of differences of reciprocals of unity. See A001242 and triangle A008969.

Links

G. C. Greubel, Table of n, a(n) for n = 0..250

Mircea Merca, Some experiments with complete and elementary symmetric functions, Periodica Mathematica Hungarica, 69 (2014), 182-189.

Formula

G.f.: 1/Product_{j=1..6} (1-6!*x/j).

a(n) = -((6!)^n)*Sum_{j=1..6} (-1)^j*binomial(6, j)/j^n, n >= 0.

a(n) = A112492(n+5, 6), n>=0.

Mathematica

T[n_, k_]:= T[n, k]= If[k==0 || k==n, 1, (k+1)^(n-k)*T[n-1, k-1] +k!*T[n-1, k]]; (* T = A112492 *)
Table[T[n+5, 5], {n, 0, 30}] (* G. C. Greubel, Jul 24 2023 *)

Prog

(PARI) a(n) = -((6!)^n)*sum(j=1, 6, (-1)^j*binomial(6, j)/j^n); \\ Michel Marcus, Apr 28 2020
(Magma)
A111886:= func< n | (-1)*Factorial(6)^n*(&+[(-1)^j*Binomial(6, j)/j^n : j in [1..6]]) >;
[A111886(n): n in [0..30]]; // G. C. Greubel, Jul 24 2023
(SageMath)
@CachedFunction
def T(n, k): # T = A112492
    if (k==0 or k==n): return 1
    else: return (k+1)^(n-k)*T(n-1, k-1) + factorial(k)*T(n-1, k)
def A111886(n): return T(n+5, 5)
[A111886(n) for n in range(31)] # G. C. Greubel, Jul 24 2023

Crossrefs

Also right-hand column 5 in triangle A008969.

Sequence in context: A205904 A061627 A232554 * A343989 A343988 A031762

Adjacent sequences: A111883 A111884 A111885 * A111887 A111888 A111889

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 12 2005

Status

approved