A336212 a(n) = Sum_{k=0..n} 3^k * binomial(n,k)^n.
1, 4, 22, 352, 19426, 3862744, 2764634356, 7403121210496, 73087416841865890, 2751096296949421766824, 387442256655054793494004132, 210421903024207931092658380560256, 431805731803048897945138363105712865124, 3443300668674111298036287560913860498279204224
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..58
Programs
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Mathematica
Table[Sum[3^k * Binomial[n, k]^n, {k, 0, n}], {n, 0, 15}] -
PARI
{a(n) = sum(k=0, n, 3^k*binomial(n, k)^n)} \\ Seiichi Manyama, Jul 13 2020
Formula
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.