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

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..58

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.

Mathematica

Table[Sum[3^k * Binomial[n, k]^n, {k, 0, n}], {n, 0, 15}]

Prog

(PARI) {a(n) = sum(k=0, n, 3^k*binomial(n, k)^n)} \\ Seiichi Manyama, Jul 13 2020

Crossrefs

Cf. A167010, A336188, A336204.

Sequence in context: A326883 A317803 A053722 * A276122 A145504 A321604

Adjacent sequences: A336209 A336210 A336211 * A336213 A336214 A336215

Keyword

nonn

Author

Vaclav Kotesovec, Jul 12 2020

Status

approved