A316145 a(n) = Sum_{k=0..n} Stirling2(n,k) * A000041(k) * k^k.

1, 9, 106, 1823, 36821, 932080, 26666067, 876727561, 32137538059, 1305168046976, 57774609056649, 2783202675369037, 144453227105110782, 8035192765567735275, 476686201707606976317, 30053582893540865299197, 2005019178999976881804130, 141111387620531900621281975

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(a(n) / A316146(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] * PartitionsP[k] * k^k, {k, 1, n}], {n, 1, 20}]

Crossrefs

Cf. A167137, A282190, A306022, A316146.

Sequence in context: A309652 A357295 A367789 * A365032 A039619 A249048

Adjacent sequences: A316142 A316143 A316144 * A316146 A316147 A316148

Keyword

nonn

Author

Vaclav Kotesovec, Jun 25 2018

Status

approved