A351282 a(n) = Sum_{k=0..n} 3^k * k^(n-k).

1, 3, 12, 48, 201, 885, 4116, 20298, 106365, 592455, 3503532, 21946620, 145210305, 1011726417, 7400390052, 56668826118, 453116188821, 3774297532467, 32682069679548, 293632972911048, 2732593851548985, 26299137526992525, 261387306941467188, 2679392140776188706

Offset

0,2

Links

Seiichi Manyama, Table of n, a(n) for n = 0..572

Formula

a(n) ~ sqrt(2*Pi/(1 + LambertW(exp(1)*n/3))) * n^(n + 1/2) * exp(n/LambertW(exp(1)*n/3) - n) / LambertW(exp(1)*n/3)^(n + 1/2).

G.f.: Sum_{k>=0} 3^k * x^k / (1 - k*x). - Ilya Gutkovskiy, Feb 06 2022

Mathematica

Join[{1}, Table[Sum[3^k*k^(n-k), {k, 0, n}], {n, 1, 25}]]

Prog

(PARI) a(n) = sum(k=0, n, 3^k*k^(n-k)); \\ Michel Marcus, Feb 06 2022

Crossrefs

Cf. A003101, A351279.

Sequence in context: A103943 A283679 A165328 * A142873 A301578 A151168

Adjacent sequences: A351279 A351280 A351281 * A351283 A351284 A351285

Keyword

nonn

Author

Vaclav Kotesovec, Feb 06 2022

Status

approved