cp's OEIS Frontend

A035277 One eighth of deca-factorial numbers.

%I A035277 #18 Dec 22 2022 04:15:46
%S A035277 1,18,504,19152,919296,53319168,3625703424,282804867072,
%T A035277 24886828302336,2438909173628928,263402190751924224,
%U A035277 31081458508727058432,3978426689117063479296,549022883098154760142848,81255386698526904501141504,12838351098367250911180357632
%N A035277 One eighth of deca-factorial numbers.
%H A035277 G. C. Greubel, <a href="/A035277/b035277.txt">Table of n, a(n) for n = 1..320</a>
%H A035277 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035277 a(n) = (Pochhammer(8/10,n)*10^n)/8.
%F A035277 8*a(n) = (10*n-2)(!^10)  = Product_{j=1..n} (10*j-2).
%F A035277 a(n) = 2^(n+2)*A034301(n) where 4*A034301(n) = (5*n-1)(!^5).
%F A035277 E.g.f.: (-1 + (1-10*x)^(-4/5))/8.
%F A035277 Sum_{n>=1} 1/a(n) = 8*(e/10^2)^(1/10)*(Gamma(4/5) - Gamma(4/5, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p A035277 seq( mul(10*j-2, j=1..n)/8, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t A035277 Table[10^n*Pochhammer[4/5, n]/8, {n,20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o A035277 (PARI) vector(20, n, prod(j=1,n, 10*j-2)/8 ) \\ _G. C. Greubel_, Nov 11 2019
%o A035277 (Magma) [(&*[10*j-2: j in [1..n]])/8: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o A035277 (Sage) [product( (10*j-2) for j in (1..n))/8 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o A035277 (GAP) List([1..20], n-> Product([1..n], j-> 10*j-2)/8 ); # _G. C. Greubel_, Nov 11 2019
%Y A035277 Cf. A034301, A045757, A035265, A035272, A035273, A035274, A035275, A035276, A035277, A035278, A035279.
%K A035277 easy,nonn
%O A035277 1,2
%A A035277 _Wolfdieter Lang_