A308565 a(n) = Sum_{k=0..n} binomial(n,k) * Stirling1(n,k) * k!.

1, 1, 0, -6, -12, 140, 1020, -5208, -117264, -2448, 17756640, 117905040, -3177424800, -56997933408, 523176632160, 25824592321920, 31907065317120, -12118922683971840, -151839867298498560, 5619086944920958464, 172859973799199892480, -1989399401447725854720, -170925579909303883614720

Offset

0,4

Links

Table of n, a(n) for n=0..22.

Formula

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

Mathematica

Table[Sum[Binomial[n, k] StirlingS1[n, k] k!, {k, 0, n}], {n, 0, 22}]
Table[n! SeriesCoefficient[(1 + Log[1 + x])^n, {x, 0, n}], {n, 0, 22}]

Crossrefs

Cf. A000312, A000522, A006252, A177380, A247075, A277759, A317274.

Sequence in context: A164584 A156432 A070020 * A341106 A203754 A002922

Adjacent sequences: A308562 A308563 A308564 * A308566 A308567 A308568

Keyword

sign

Author

Ilya Gutkovskiy, Jun 07 2019

Status

approved