A132961 Total number of all distinct cycle sizes in all permutations of [n].

1, 2, 9, 38, 215, 1384, 10409, 86946, 825075, 8541998, 97590779, 1205343952, 16148472977, 231416203212, 3560209750005, 58104163643054, 1008693571819919, 18477578835352366, 357476371577422955, 7258865626801695048, 154893910336866444009, 3454112338490001478772

Offset: 1

Author

Vladeta Jovovic, Sep 06 2007

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..450

Crossrefs

Cf. A000254, A132958, A132959, A132960, A132962, A132963.

Row sums of A293211.

Programs

Maple

with(combinat):
b:= proc(n, i) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add(multinomial(n, n-i*j, i$j)/j!*(i-1)!^j*(p-> p+
      [0, p[1]*`if`(j>0, 1, 0)])(b(n-i*j, i-1)), j=0..n/i)))
    end:
a:= n-> b(n$2)[2]:
seq(a(n), n=1..30);  # Alois P. Heinz, Oct 21 2015

Mathematica

Rest[ Range[0, 22]! CoefficientList[ Series[1/(1 - x) Sum[1 - Exp[ -x^k/k], {k, 25}], {x, 0, 22}], x]] (* Robert G. Wilson v, Sep 13 2007 *)

Formula

E.g.f.: 1/(1-x)*Sum_{k>0} (1-exp(-x^k/k)). Exponential convolution of A132960(n) and n!: a(n) = n!*Sum_{k=1..n} A132960(k)/k!.

Extensions

More terms from Robert G. Wilson v, Sep 13 2007