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