A332944 Number of entries in the fourth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

1, 21, 166, 1247, 7855, 47245, 284968, 1741235, 10782872, 69537976, 471717130, 3336898255, 24584784957, 189704257763, 1530649634720, 12849873769593, 111945035887787, 1011184665775833, 9458811859041042, 91480934118104305, 913112230809837136, 9391472034599656856

Offset: 4

Author

Alois P. Heinz, Mar 03 2020

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..576
• Wikipedia, Partition of a set

Crossrefs

Column k=4 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, 4)[2]:
seq(a(n), n=4..25);