A333065 Number of entries in the eighth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 37, 796, 13091, 183074, 2300949, 26869727, 298009584, 3190196105, 33408754043, 346447486658, 3596858467639, 37729664292626, 402420037089997, 4378064125023471, 48598561597491856, 549602546782048959, 6318831653757436761, 73723789208978689966

Offset: 8

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..576
• Wikipedia, Partition of a set

Crossrefs

Column k=8 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, 8)[2]:
seq(a(n), n=8..26);