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A331341 a(n) = n! * [x^n] 1 / (1 - Sum_{k=1..n} log(1 + k*x)). 2

%I

%S 1,1,13,864,151276,55463850,36662614458,39635566403328,

%T 65354864056231104,155978053040893370400,517297066212058929642000,

%U 2307448887344816064221408256,13478142770116878179295616074624,100820731073923375628659569173854704

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

%H Vaclav Kotesovec, <a href="/A331341/b331341.txt">Table of n, a(n) for n = 0..167</a>

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

%F a(n) ~ sqrt(Pi) * n^(3*n + 1/2) / (2^(n - 1/2) * exp(n - 1/3)). - _Vaclav Kotesovec_, Jan 28 2020

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

%t 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}]

%Y Cf. A006252, A319508, A319509, A331340.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 14 2020

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Last modified September 24 04:42 EDT 2020. Contains 337317 sequences. (Running on oeis4.)