A270495 Sum of the sizes of the third blocks in all set partitions of {1,2,...,n}.

1, 8, 47, 253, 1345, 7304, 41193, 243152, 1506521, 9799547, 66844755, 477297022, 3560469469, 27692022408, 224128400923, 1884299045789, 16427961558365, 148293477761232, 1384008870213057, 13336887952918752, 132535336519342301, 1356662080571809755

Offset: 3

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..575
• Wikipedia, Partition of a set

Crossrefs

Column p=3 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<4, [p[1], p[2]+p[1]*x^j], p))(
       b(n-1, max(m, j))), j=1..m+1))
    end:
a:= n-> coeff(b(n, 0)[2], x, 3):
seq(a(n), n=3..25);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 4, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
a[n_] := Coefficient[b[n, 0][[2]], x, 3];
Table[a[n], {n, 3, 25}] (* Jean-François Alcover, May 27 2018, translated from Maple *)