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%I #8 Feb 12 2024 05:56:40
%S 1,1,2,6,12,20,360,2520,1680,15120,151200,554400,9979200,129729600,
%T 605404800,27243216000,54486432000,308756448000,5557616064000,
%U 8122669632000,351982350720000,22174888095360000,25676186215680000,3740164458750720000,67322960257512960000
%N Denominator of the sum of inverse products of cycle sizes in all permutations of [n].
%H Alois P. Heinz, <a href="/A323291/b323291.txt">Table of n, a(n) for n = 0..505</a>
%F E.g.f.: exp(polylog(2,x)) (for fractions A323290(n)/A323291(n)). - _Vaclav Kotesovec_, Feb 12 2024
%p b:= proc(n) option remember; `if`(n=0, 1, add(
%p b(n-j)*binomial(n-1, j-1)*(j-1)!/j, j=1..n))
%p end:
%p a:= n-> denom(b(n)):
%p seq(a(n), n=0..25);
%t nmax = 30; Denominator[CoefficientList[Series[Exp[PolyLog[2, x]], {x, 0, nmax}], x] * Range[0, nmax]!] (* _Vaclav Kotesovec_, Feb 12 2024 *)
%Y See A323290 for more information.
%K nonn,frac
%O 0,3
%A _Alois P. Heinz_, Jan 09 2019