A333067 Number of entries in the tenth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 56, 1772, 41835, 822277, 14253254, 225620777, 3337585487, 46894138343, 633327676249, 8297945378872, 106274752981884, 1339352574256161, 16713308238007881, 207742699406820799, 2586686884152971976, 32427925119758431591, 410991858695177722552

Offset: 10

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..576
• Wikipedia, Partition of a set

Crossrefs

Column k=10 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, 10)[2]:
seq(a(n), n=10..27);