A114917 Number of partitions of {1,..,n} in which no part of a given size occurs just once.

1, 0, 1, 1, 4, 1, 71, 106, 1051, 2759, 19552, 51041, 864579, 3134132, 34990671, 211464345, 1832236004, 11261632321, 109973219879, 659853699654, 8379292553185, 58134013363151, 676374746166550, 5912498819726335, 71622214447120275, 658455096592878092

Offset: 0

Author

Christian G. Bower, Jan 06 2006

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..576

Crossrefs

Cf. A000110, A007690, A360182.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
      add(`if`(j=1, 0, b(n-i*j, i-1)*combinat[multinomial]
              (n, n-i*j, i$j)/j!), j=0..min(n/i))))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..26);  # Alois P. Heinz, May 14 2023

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[If[j == 1, 0, b[n - i*j, i - 1]*multinomial[n, Prepend[Table[i, {j}], n - i*j]]/j!], {j, 0, Min[n/i]}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 26}] (* Jean-François Alcover, May 26 2023, after Alois P. Heinz *)