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.

A345646 a(n) = Sum_{k=0..n} (4*n)! / (k! * (n-k)!)^4.

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%I A345646 #10 Jun 21 2021 10:02:03
%S A345646 1,48,45360,60614400,114144030000,249344297250048,609148118181867264,
%T A345646 1604207350254328934400,4471935609925802450718000,
%U A345646 13022708340511827298941600000,39267738740263529465273799855360,121811974529188978353365962361671680,386880842128109815466159332537704902400
%N A345646 a(n) = Sum_{k=0..n} (4*n)! / (k! * (n-k)!)^4.
%C A345646 In general, for fixed m >= 1, Sum_{k=0..n} (m*n)! / (k!*(n-k)!)^m ~ (2*m)^(m*n) / (Pi*n)^(m-1).
%H A345646 Seiichi Manyama, <a href="/A345646/b345646.txt">Table of n, a(n) for n = 0..279</a>
%F A345646 a(n) ~ 2^(12*n) / (Pi*n)^3.
%t A345646 Table[Sum[(4*n)! / (k! * (n-k)!)^4, {k, 0, n}], {n, 0, 15}]
%Y A345646 Column 4 of A306641.
%Y A345646 Cf. A306642, A306644.
%K A345646 nonn
%O A345646 0,2
%A A345646 _Vaclav Kotesovec_, Jun 21 2021