A316146 a(n) = Sum_{k=0..n} Stirling2(n,k) * A000009(k) * k^k.

1, 5, 67, 865, 15906, 365514, 9545026, 276368635, 9188742238, 343857717788, 13998751394662, 618098575755637, 29469995998980356, 1510585321262760900, 83100039017148288635, 4873627957977247842223, 302388593396139280682588, 19804146883678522219587314

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..370

Formula

Limit_{n -> infinity} (a(n)/n!)^(1/n) = 1/(log(1+ exp(1)) - 1) = 3.1922192845297391106277924019427161296056687330974482534324... - Vaclav Kotesovec, Nov 21 2021

log(A316145(n) / a(n)) ~ (sqrt(2) - 1) * Pi * sqrt(n) / sqrt(3*(1 + exp(1)) * log(1 + exp(-1))). - Vaclav Kotesovec, Nov 22 2021

Mathematica

Table[Sum[StirlingS2[n, k] * PartitionsQ[k] * k^k, {k, 1, n}], {n, 1, 20}]

Crossrefs

Cf. A282190, A305550, A306023, A316145.

Sequence in context: A226343 A067393 A212731 * A113265 A124435 A123034

Adjacent sequences: A316143 A316144 A316145 * A316147 A316148 A316149

Keyword

nonn

Author

Vaclav Kotesovec, Jun 25 2018

Status

approved