A333064 Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 29, 499, 6676, 77078, 810470, 8016373, 76334142, 713507667, 6658565009, 62882380589, 606149817728, 5983648334738, 60440402586898, 622934996801505, 6532386995235676, 69575530733726891, 752420279343383619, 8269751757387345271, 92538014365261646366

Offset: 7

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..576
• Wikipedia, Partition of a set

Crossrefs

Column k=7 of A319375.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
      add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
       combinat[multinomial](n, i$j, n-i*j)/j!*
      b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
    end:
a:= n-> b(n$2, 7)[2]:
seq(a(n), n=7..26);