A317172 a(n) = n! * [x^n] 1/(1 - n*log(1 + x)).

1, 1, 6, 114, 4168, 248870, 21966768, 2685571560, 434202400896, 89679267601632, 23032451508686400, 7199033431349412576, 2690461258552995849216, 1184680716090974803461072, 606986901206377433194091520, 358023049940533240478842992000, 240858598980174362552808566194176

Offset: 0

Author

Ilya Gutkovskiy, Jul 23 2018

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A006252, A088501, A094420, A242817, A317171.

Main diagonal of A320080.

Programs

Mathematica

Table[n! SeriesCoefficient[1/(1 - n Log[1 + x]), {x, 0, n}], {n, 0, 16}]
Join[{1}, Table[Sum[StirlingS1[n, k] n^k k!, {k, n}], {n, 16}]]

PARI

{a(n) = sum(k=0, n, k!*n^k*stirling(n, k, 1))} \\ Seiichi Manyama, Jun 12 2020

Formula

a(n) = Sum_{k=0..n} Stirling1(n,k)*n^k*k!.

a(n) ~ sqrt(2*Pi) * n^(2*n + 1/2) / exp(n + 1/2). - Vaclav Kotesovec, Jul 23 2018