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A331340 a(n) = n! * [x^n] 1 / (1 + Sum_{k=1..n} log(1 - k*x)). 2
1, 1, 23, 1872, 371524, 147316050, 102823452318, 115685840003328, 196669439127051840, 480847207762313690400, 1626231663646322798946000, 7372321556702072183715972096, 43653032698484678876818157764224, 330351436922959495109028135649934640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vaclav Kotesovec, Table of n, a(n) for n = 0..167

FORMULA

a(n) = n! * [x^n] 1 / (1 + log(Sum_{k=0..n} Stirling1(n+1,n-k+1) * x^k)).

a(n) ~ sqrt(Pi) * n^(3*n + 1/2) / (2^(n - 1/2) * exp(n - 5/3)). - Vaclav Kotesovec, Jan 28 2020

MATHEMATICA

Table[n! SeriesCoefficient[1/(1 + Sum[Log[1 - k x], {k, 1, n}]), {x, 0, n}], {n, 0, 13}]

Table[n! SeriesCoefficient[1/(1 + Log[Sum[StirlingS1[n + 1, n - k + 1] x^k, {k, 0, n}]]), {x, 0, n}], {n, 0, 13}]

CROSSREFS

Cf. A007840, A319508, A319509, A331341.

Sequence in context: A229814 A326365 A319508 * A269122 A132395 A064016

Adjacent sequences:  A331337 A331338 A331339 * A331341 A331342 A331343

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Jan 14 2020

STATUS

approved

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Last modified September 24 11:30 EDT 2020. Contains 337318 sequences. (Running on oeis4.)