cp's OEIS Frontend

A272603 Number of permutations of [n] whose cycle lengths are factorials.

%I A272603 #18 Jul 22 2018 11:35:09
%S A272603 1,1,2,4,10,26,196,1072,7484,42940,261496,1477136,15219832,134828344,
%T A272603 1488515120,13692017536,130252442896,1123580329232,14639510308384,
%U A272603 173489066401600,2528654220104096,31472160333513376,402634734214583872,4645625988351336704,25925035549644280991680
%N A272603 Number of permutations of [n] whose cycle lengths are factorials.
%H A272603 Alois P. Heinz, <a href="/A272603/b272603.txt">Table of n, a(n) for n = 0..455</a>
%F A272603 E.g.f.: exp( sum(n>=1, x^(n!) / n! ) ).
%p A272603 a:= proc(n) option remember; local r, f, i;
%p A272603       if n=0 then 1 else r, f, i:= $0..2;
%p A272603         while f<=n do r:= r +a(n-f)*(f-1)!*
%p A272603           binomial(n-1, f-1); f, i:= f*i, i+1
%p A272603         od; r
%p A272603       fi
%p A272603     end:
%p A272603 seq(a(n), n=0..25);  # _Alois P. Heinz_, Jun 04 2016
%t A272603 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 *)
%o A272603 (PARI) N=66; x='x+O('x^N); Vec(serlaplace(exp(sum(n=1,10,x^(n!)/n!))))
%Y A272603 Cf. A000142, A273001 (cycle lengths are Fibonacci numbers), A272602 (e.g.f.: exp( sum(n>=1, x^(n!) / n ) ) ), A273996, A317132.
%K A272603 nonn
%O A272603 0,3
%A A272603 _Joerg Arndt_, May 29 2016