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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..5000

Wikipedia, Partition of a set

Formula

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

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

Maple

b:= proc(n, i, k) option remember; `if`(i*(i+1)/2<n, 0,
      `if`(n=0, k, b(n, i-1, k)+(t-> 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 *)

Crossrefs

Cf. A003056, A330460, A330759.

Sequence in context: A238389 A115292 A202676 * A336718 A173324 A318243

Adjacent sequences: A330762 A330763 A330764 * A330766 A330767 A330768

Keyword

nonn

Author

Alois P. Heinz, Dec 29 2019

Status

approved