A333066 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

1, 46, 1211, 24047, 401337, 5957407, 81381744, 1046405027, 12866407790, 153103993523, 1780561219354, 20417258320972, 232758457316938, 2658399095977056, 30621521649045981, 357523836553565584, 4243836001737759231, 51265500225372571466, 629904897694885693327

Offset: 9

Author

Alois P. Heinz, Mar 06 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..576
• Wikipedia, Partition of a set

Crossrefs

Column k=9 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, 9)[2]:
seq(a(n), n=9..27);