A034976 One eighth of octo-factorial numbers.

1, 16, 384, 12288, 491520, 23592960, 1321205760, 84557168640, 6088116142080, 487049291366400, 42860337640243200, 4114592413463347200, 427917611000188108800, 47926772432021068185600, 5751212691842528182272000, 736155224555843607330816000

Offset: 1

Author

Wolfdieter Lang

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..325
• Index entries for sequences related to factorial numbers.

Crossrefs

Cf. A034908, A034909, A034910, A034911, A034912, A034975, A045755, A051189.

Programs

Magma

[8^(n-1)*Factorial(n): n in [1..40]]; // G. C. Greubel, Oct 20 2022

Mathematica

Table[8^(n-1)*n!, {n,40}] (* G. C. Greubel, Oct 20 2022 *)

SageMath

[8^(n-1)*factorial(n) for n in range(1,40)] # G. C. Greubel, Oct 20 2022

Formula

8*a(n) = (8*n)!^8 = Product_{j=1..n} 8*j = 8^n*n!.

E.g.f.: (-1+(1-8*x)^(-1))/8.

G.f.: x/(1-16*x/(1-8*x/(1-24*x/(1-16*x/(1-32*x/(1-24*x/(1-40*x/(1-32*x/(1-... (continued fraction). - Philippe Deléham, Jan 07 2012

From Amiram Eldar, Jan 08 2022: (Start)

Sum_{n>=1} 1/a(n) = 8*(exp(1/8)-1).

Sum_{n>=1} (-1)^(n+1)/a(n) = 8*(1-exp(-1/8)). (End)