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A317171 a(n) = n! * [x^n] 1/(1 + n*log(1 - x)). 2
1, 1, 10, 222, 8824, 553870, 50545008, 6328330344, 1041597412224, 218138133235680, 56650689388344000, 17868469522986145536, 6728682216722958185472, 2981868816113406609186576, 1536217706761623823662025728, 910442461680276910819097616000, 615053979239579281793375485526016 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..16.

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

MATHEMATICA

Table[n! SeriesCoefficient[1/(1 + n Log[1 - x]), {x, 0, n}], {n, 0, 16}]

Join[{1}, Table[Sum[Abs[StirlingS1[n, k]] n^k k!, {k, n}], {n, 16}]]

CROSSREFS

Cf. A007840, A088500, A094420, A242817, A317172.

Main diagonal of A320079.

Sequence in context: A210137 A064333 A223817 * A229256 A052789 A092254

Adjacent sequences:  A317168 A317169 A317170 * A317172 A317173 A317174

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jul 23 2018

STATUS

approved

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Last modified December 2 03:22 EST 2020. Contains 338865 sequences. (Running on oeis4.)