A332948 Number of entries in the eighth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 73, 1666, 31241, 486377, 6638568, 82413787, 961757669, 10756109317, 116409307679, 1228840258412, 12766418662681, 131564790987337, 1352403410824806, 13925656629847559, 144227711099572501, 1508401366805906552, 15986784485974156076, 172225656206792090516

Offset: 8

Author

Alois P. Heinz, Mar 03 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 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, 8)[2]:
seq(a(n), n=8..26);