A270498 Sum of the sizes of the sixth blocks in all set partitions of {1,2,...,n}.

1, 23, 324, 3645, 36223, 334751, 2965654, 25691104, 220643295, 1897548384, 16463907354, 144927422746, 1299763249771, 11912250951457, 111803042249042, 1076045623549383, 10628068291940557, 107760039986995689, 1121581530251066296, 11980190581723881858

Offset: 6

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..575
• Wikipedia, Partition of a set

Crossrefs

Column p=6 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<7, [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, 6):
seq(a(n), n=6..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 7, {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, 6];
Table[a[n], {n, 6, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)