A323291 Denominator of the sum of inverse products of cycle sizes in all permutations of [n].

1, 1, 2, 6, 12, 20, 360, 2520, 1680, 15120, 151200, 554400, 9979200, 129729600, 605404800, 27243216000, 54486432000, 308756448000, 5557616064000, 8122669632000, 351982350720000, 22174888095360000, 25676186215680000, 3740164458750720000, 67322960257512960000

Offset: 0

Author

Alois P. Heinz, Jan 09 2019

Keywords

• nonn
• frac

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..505

Crossrefs

See A323290 for more information.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, add(
      b(n-j)*binomial(n-1, j-1)*(j-1)!/j, j=1..n))
    end:
a:= n-> denom(b(n)):
seq(a(n), n=0..25);

Mathematica

nmax = 30; Denominator[CoefficientList[Series[Exp[PolyLog[2, x]], {x, 0, nmax}], x] * Range[0, nmax]!] (* Vaclav Kotesovec, Feb 12 2024 *)

Formula

E.g.f.: exp(polylog(2,x)) (for fractions A323290(n)/A323291(n)). - Vaclav Kotesovec, Feb 12 2024