A272603 Number of permutations of [n] whose cycle lengths are factorials.
1, 1, 2, 4, 10, 26, 196, 1072, 7484, 42940, 261496, 1477136, 15219832, 134828344, 1488515120, 13692017536, 130252442896, 1123580329232, 14639510308384, 173489066401600, 2528654220104096, 31472160333513376, 402634734214583872, 4645625988351336704, 25925035549644280991680
Offset: 0
Keywords
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..455
Crossrefs
Programs
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Maple
a:= proc(n) option remember; local r, f, i; if n=0 then 1 else r, f, i:= $0..2; while f<=n do r:= r +a(n-f)*(f-1)!* binomial(n-1, f-1); f, i:= f*i, i+1 od; r fi end: seq(a(n), n=0..25); # Alois P. Heinz, Jun 04 2016 -
Mathematica
nmax = 4; egf = Exp[Sum[x^n!/n!, {n, 1, nmax}]] + O[x]^(nmax! + 1); CoefficientList[egf, x]*Range[0, nmax!]! (* Jean-François Alcover, Feb 19 2017 *) -
PARI
N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(n=1,10,x^(n!)/n!))))
Formula
E.g.f.: exp( sum(n>=1, x^(n!) / n! ) ).