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%I #10 Jul 13 2020 06:19:20
%S 1,4,22,352,19426,3862744,2764634356,7403121210496,73087416841865890,
%T 2751096296949421766824,387442256655054793494004132,
%U 210421903024207931092658380560256,431805731803048897945138363105712865124,3443300668674111298036287560913860498279204224
%N a(n) = Sum_{k=0..n} 3^k * binomial(n,k)^n.
%H Seiichi Manyama, <a href="/A336212/b336212.txt">Table of n, a(n) for n = 0..58</a>
%F a(n) ~ c * exp(-1/4) * 2^(n^2 + n/2) * (3/(Pi*n))^(n/2), where c = Sum_{k = -infinity..infinity} 3^k * exp(-2*k^2) = 1.4541744598397064657680975624481... if n is even and c = Sum_{k = -infinity..infinity} 3^(k + 1/2) * exp(-2*(k + 1/2)^2) = 1.4606428581939532945566671970305... if n is odd.
%t Table[Sum[3^k * Binomial[n, k]^n, {k, 0, n}], {n, 0, 15}]
%o (PARI) {a(n) = sum(k=0, n, 3^k*binomial(n, k)^n)} \\ _Seiichi Manyama_, Jul 13 2020
%Y Cf. A167010, A336188, A336204.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jul 12 2020
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