A330765 Total number of blocks in all set partitions of strict integer partitions of n.

0, 1, 1, 4, 4, 7, 17, 20, 30, 43, 90, 103, 160, 210, 304, 515, 646, 894, 1223, 1659, 2176, 3484, 4226, 5873, 7638, 10335, 13150, 17695, 24974, 31394, 41383, 53766, 69718, 89573, 115613, 146344, 201625, 247880, 322099, 406445, 524634, 654298, 839584, 1043012

Offset: 0

Author

Alois P. Heinz, Dec 29 2019

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..5000
• Wikipedia, Partition of a set

Crossrefs

Cf. A003056, A330460, A330759.

Programs

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+1)/2 b(n-i, t, k)*k
        +b(n-i, t, k+1))(min(n-i, i-1))))
    end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..50);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[i(i+1)/2 < n, 0, If[n==0, k, b[n, i-1, k] + b[n-i, #, k] k + b[n-i, #, k+1]&[Min[n-i, i-1]]]];
a[n_] := b[n, n, 0];
a /@ Range[0, 50] (* Jean-François Alcover, May 08 2020, after Maple *)

Formula

a(n) = Sum_{k=1..A003056(n)} k * A330460(n,k).

a(n) = Sum_{k=1..A003056(n)} k * A330759(n,k).