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

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..576

Wikipedia, Partition of a set

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);

Crossrefs

Column k=4 of A319298.

Sequence in context: A146301 A338891 A126993 * A022681 A266733 A107970

Adjacent sequences: A332941 A332942 A332943 * A332945 A332946 A332947

Keyword

nonn

Author

Alois P. Heinz, Mar 03 2020

Status

approved