A332949 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 91, 2531, 56717, 1052130, 17011450, 248006774, 3363718597, 43354519587, 537399621668, 6456347423794, 75743936924077, 874027443321519, 9978667891988711, 113225455087566673, 1281748270131892718, 14527578406583077101, 165413377044356558731

Offset: 9

Author

Alois P. Heinz, Mar 03 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 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, 9)[2]:
seq(a(n), n=9..26);