A111888 Eighth column of triangle A112492 (inverse scaled Pochhammer symbols).

1, 109584, 7245893376, 381495483224064, 17810567950611972096, 778101042571221893382144, 32762625292956765972873609216, 1351813956241264848815287984717824

Offset

0,2

Comments

Also continuation of family of Differences of reciprocals of unity. See A001242, A111887 and triangle A008969.

Links

Table of n, a(n) for n=0..7.

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

Formula

G.f.: 1/Product_{j=1..8} 1-8!*x/j.

a(n) = -((8!)^n) * Sum_{j=1..8} (-1)^j*binomial(8, j)/j^n, n>=0.

a(n) = A112492(n+7, 8), 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+7, 7], {n, 0, 30}] (* G. C. Greubel, Jul 24 2023 *)

Prog

(PARI) a(n) = -((8!)^n)*sum(j=1, 8, ((-1)^j)*binomial(8, j)/j^n); \\ Michel Marcus, Apr 28 2020
(Magma)
A111888:= func< n | (-1)*Factorial(8)^n*(&+[(-1)^j*Binomial(8, j)/j^n : j in [1..8]]) >;
[A111888(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 A111888(n): return T(n+7, 7)
[A111888(n) for n in range(31)] # G. C. Greubel, Jul 24 2023

Crossrefs

Also right-hand column 7 in triangle A008969.

Cf. A001242, A111887, A112492.

Sequence in context: A237963 A234700 A238061 * A183770 A023349 A368020

Adjacent sequences: A111885 A111886 A111887 * A111889 A111890 A111891

Keyword

nonn,easy

Author

Wolfdieter Lang, Sep 12 2005

Status

approved