A332946 Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 43, 617, 7681, 79756, 741665, 6467891, 54658254, 451897330, 3685879069, 30091146181, 248749105815, 2091117462980, 17933165800591, 157654535847037, 1426401197217090, 13303368764700743, 127934361462621048, 1268098183967052868, 12948542410221048226

Offset: 6

Author

Alois P. Heinz, Mar 03 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..576
• Wikipedia, Partition of a set

Crossrefs

Column k=6 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, 6)[2]:
seq(a(n), n=6..25);