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.

A035272 One third of deca-factorial numbers.

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%I A035272 #18 Dec 22 2022 04:15:53
%S A035272 1,13,299,9867,424281,22486893,1416674259,103417220907,8583629335281,
%T A035272 798277528181133,82222585402656699,9291152150500206987,
%U A035272 1142811714511525459401,151993958030032886100333,21735135998294702712347619,3325475807739089514989185707,542052556661471590943237270241
%N A035272 One third of deca-factorial numbers.
%H A035272 G. C. Greubel, <a href="/A035272/b035272.txt">Table of n, a(n) for n = 1..320</a>
%H A035272 <a href="/index/Fa#factorial">Index entries for sequences related to factorial numbers</a>.
%F A035272 3*a(n) = (10*n-7)(!^10) = Product_{j=1..n} (10*j-7).
%F A035272 E.g.f.: (-1 + (1-10*x)^(-3/10))/3.
%F A035272 Sum_{n>=1} 1/a(n) = 3*(e/10^7)^(1/10)*(Gamma(3/10) - Gamma(3/10, 1/10)). - _Amiram Eldar_, Dec 22 2022
%p A035272 seq( mul(10*j-7, j=1..n)/3, n=1..20); # _G. C. Greubel_, Nov 11 2019
%t A035272 Table[10^n*Pochhammer[3/10, n]/3, {n, 20}] (* _G. C. Greubel_, Nov 11 2019 *)
%o A035272 (PARI) vector(20, n, prod(j=1,n, 10*j-7)/3 ) \\ _G. C. Greubel_, Nov 11 2019
%o A035272 (Magma) [(&*[10*j-7: j in [1..n]])/3: n in [1..20]]; // _G. C. Greubel_, Nov 11 2019
%o A035272 (Sage) [product( (10*j-7) for j in (1..n))/3 for n in (1..20)] # _G. C. Greubel_, Nov 11 2019
%o A035272 (GAP) List([1..20], n-> Product([1..n], j-> 10*j-7)/3 ); # _G. C. Greubel_, Nov 11 2019
%Y A035272 Cf. A035273, A035274, A035275, A035276, A035277, A035278, A035279, A045757.
%K A035272 easy,nonn
%O A035272 1,2
%A A035272 _Wolfdieter Lang_