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%I #11 Nov 25 2017 03:46:25
%S 1,3,40,8105,24053106,1016507243472,622366942086680904,
%T 5608321882919220905812521,752711651805019773658037206391596,
%U 1518219710649896586598445898967340890577318,46343146356260529633020448755386347142785083052620084
%N a(n) = Sum_{k=0..n} binomial(n+k,k)^k.
%H Seiichi Manyama, <a href="/A295612/b295612.txt">Table of n, a(n) for n = 0..41</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>
%F a(n) = Sum_{k=0..n} A046899(n,k)^k.
%F a(n) ~ 2^(2*n^2) / (exp(1/8) * Pi^(n/2) * n^(n/2)). - _Vaclav Kotesovec_, Nov 25 2017
%t Table[Sum[Binomial[n + k, k]^k, {k, 0, n}], {n, 0, 10}]
%t Table[Sum[((n + k)!/(n! k!))^k, {k, 0, n}], {n, 0, 10}]
%o (PARI) a(n) = sum(k=0, n, binomial(n+k,k)^k); \\ _Michel Marcus_, Nov 25 2017
%Y Cf. A001700, A046899, A112028, A112029, A167008, A219562, A219563, A219564.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Nov 24 2017
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