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One eighth of octo-factorial numbers.
6

%I #30 Oct 21 2022 06:58:32

%S 1,16,384,12288,491520,23592960,1321205760,84557168640,6088116142080,

%T 487049291366400,42860337640243200,4114592413463347200,

%U 427917611000188108800,47926772432021068185600,5751212691842528182272000,736155224555843607330816000

%N One eighth of octo-factorial numbers.

%H G. C. Greubel, <a href="/A034976/b034976.txt">Table of n, a(n) for n = 1..325</a>

%H <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.

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

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

%F 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

%F From _Amiram Eldar_, Jan 08 2022: (Start)

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

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

%t Table[8^(n-1)*n!, {n,40}] (* _G. C. Greubel_, Oct 20 2022 *)

%o (Magma) [8^(n-1)*Factorial(n): n in [1..40]]; // _G. C. Greubel_, Oct 20 2022

%o (SageMath) [8^(n-1)*factorial(n) for n in range(1,40)] # _G. C. Greubel_, Oct 20 2022

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

%K easy,nonn

%O 1,2

%A _Wolfdieter Lang_