A331341 a(n) = n! * [x^n] 1 / (1 - Sum_{k=1..n} log(1 + k*x)).
1, 1, 13, 864, 151276, 55463850, 36662614458, 39635566403328, 65354864056231104, 155978053040893370400, 517297066212058929642000, 2307448887344816064221408256, 13478142770116878179295616074624, 100820731073923375628659569173854704
Offset: 0
Keywords
Links
- Vaclav Kotesovec, Table of n, a(n) for n = 0..167
Programs
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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[Abs[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 - 1/3)). - Vaclav Kotesovec, Jan 28 2020