A132963 Total number of distinct block sizes in all partitions of [n].

1, 2, 8, 25, 102, 439, 2067, 10406, 56754, 328257, 2015818, 13067366, 89192170, 638321285, 4779442602, 37332643831, 303635437532, 2565592977205, 22483754207839, 204013083946460, 1913880812797792, 18536832515581167, 185130415180288134, 1904280138346826637

Offset: 1

Author

Vladeta Jovovic, Sep 06 2007

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A005493, A132958, A132959, A132960, A132961, A132962, A350175.

Programs

Maple

b:= proc(n, i, c) option remember; `if`(n=0, c,
      `if`(i<1, 0, add(b(n-j*i, i-1, c+signum(j))*
      combinat[multinomial](n, n-i*j, i$j)/j!, j=0..n/i)))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=1..30);  # Alois P. Heinz, Jan 06 2022

Mathematica

Rest[ Range[0, 23]! CoefficientList[ Series[ Exp[ Exp[x] - 1] Sum[1 - Exp[ -x^k/k! ], {k, 30}], {x, 0, 23}], x]] (* Robert G. Wilson v, Sep 13 2007 *)

Formula

E.g.f.: exp(exp(x)-1)*Sum_{k>0} (1-exp(-x^k/k!)).

Extensions

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