cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A035273 One quarter of deca-factorial numbers.

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%I A035273 #20 Dec 22 2022 07:22:28
%S A035273 1,14,336,11424,502656,27143424,1737179136,128551256064,
%T A035273 10798305509376,1015040717881344,105564234659659776,
%U A035273 12034322751201214464,1492256021148950593536,199962306833959379533824,28794572184090150652870656,4434364116349883200542081024
%N A035273 One quarter of deca-factorial numbers.
%H A035273 G. C. Greubel, <a href="/A035273/b035273.txt">Table of n, a(n) for n = 1..320</a>
%H A035273 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035273 4*a(n) = (10*n-6)(!^10) = Product_{j=1..n} (10*j-6).
%F A035273 a(n) = 2^(n+1)*A034323(n) where 2*A034323(n)= (5*n-3)(!^5) = Product_{j=1..n} (5*j-3).
%F A035273 E.g.f.: (-1 + (1-10*x)^(-2/5))/4.
%F A035273 a(n) = (Pochhammer(4/10,n)*10^n)/4.
%F A035273 Sum_{n>=1} 1/a(n) = 4*(e/10^6)^(1/10)*(Gamma(2/5) - Gamma(2/5, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p A035273 seq( mul(10*j-6, j=1..n)/4, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t A035273 Table[10^n*Pochhammer[4/10, n]/4, {n,20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o A035273 (PARI) vector(20, n, prod(j=1,n, 10*j-6)/4 ) \\ _G. C. Greubel_, Nov 11 2019
%o A035273 (Magma) [(&*[10*j-6: j in [1..n]])/4: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o A035273 (Sage) [product( (10*j-6) for j in (1..n))/4 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o A035273 (GAP) List([1..20], n-> Product([1..n], j-> 10*j-6)/4 ); # _G. C. Greubel_, Nov 11 2019
%Y A035273 Cf. A034323, A035272, A035274, A035275, A035276, A035277, A035278, A035279, A045757.
%K A035273 easy,nonn
%O A035273 1,2
%A A035273 _Wolfdieter Lang_