A270497 Sum of the sizes of the fifth blocks in all set partitions of {1,2,...,n}.

1, 17, 184, 1641, 13276, 102244, 770989, 5795889, 43967302, 339403001, 2681449074, 21763977864, 181900742989, 1567473197429, 13932812925824, 127738400615689, 1207445992487256, 11759938209394472, 117926100082535985, 1216563820893322317, 12901060857158377838

Offset: 5

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..575
• Wikipedia, Partition of a set

Crossrefs

Column p=5 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<6, [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, 5):
seq(a(n), n=5..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 6, {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, 5];
Table[a[n], {n, 5, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)