A332945 Number of entries in the fifth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 31, 337, 3305, 27085, 203278, 1470470, 10525307, 74735025, 534251602, 3917281240, 29620189877, 230717097457, 1858373700800, 15544789470865, 135021858204377, 1215283222207344, 11317462847981403, 108929278516177839, 1082642589072326140, 11099778977689173356

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..576

Wikipedia, Partition of a set

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
      max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
    end:
a:= n-> b(n, 1, 5)[2]:
seq(a(n), n=5..25);

Crossrefs

Column k=5 of A319298.

Sequence in context: A111675 A142495 A100728 * A296730 A274180 A197644

Adjacent sequences: A332942 A332943 A332944 * A332946 A332947 A332948

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2020

Status

approved