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

Author

Alois P. Heinz, Mar 03 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..576
• Wikipedia, Partition of a set

Crossrefs

Column k=5 of A319298.

Programs

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);