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

0,5

Links

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

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 *)

Crossrefs

Cf. A000110, A007690, A360182.

Sequence in context: A069740 A173008 A298828 * A100864 A295178 A255192

Adjacent sequences: A114914 A114915 A114916 * A114918 A114919 A114920

Keyword

nonn

Author

Christian G. Bower, Jan 06 2006

Status

approved