A331340 a(n) = n! * [x^n] 1 / (1 + Sum_{k=1..n} log(1 - k*x)).

1, 1, 23, 1872, 371524, 147316050, 102823452318, 115685840003328, 196669439127051840, 480847207762313690400, 1626231663646322798946000, 7372321556702072183715972096, 43653032698484678876818157764224, 330351436922959495109028135649934640

Offset: 0

Author

Ilya Gutkovskiy, Jan 14 2020

Keywords

• nonn

Links

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

Crossrefs

Cf. A007840, A319508, A319509, A331341.

Programs

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}]

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