A331340 - OEIS

%I #8 Jan 28 2020 04:51:43

%S 1,1,23,1872,371524,147316050,102823452318,115685840003328,

%T 196669439127051840,480847207762313690400,1626231663646322798946000,

%U 7372321556702072183715972096,43653032698484678876818157764224,330351436922959495109028135649934640

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

%H Vaclav Kotesovec, <a href="/A331340/b331340.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 - 5/3)). - _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[StirlingS1[n + 1, n - k + 1] x^k, {k, 0, n}]]), {x, 0, n}], {n, 0, 13}]

%Y Cf. A007840, A319508, A319509, A331341.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 14 2020