A270499 Sum of the sizes of the seventh blocks in all set partitions of {1,2,...,n}.

1, 30, 536, 7473, 90223, 995191, 10354804, 103779309, 1016654053, 9840330258, 94884791378, 917358452410, 8938608738199, 88139900141632, 882388425916186, 8991438542446875, 93434278760386701, 991477889069432577, 10753621593467498170, 119276548511953973463

Offset: 7

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..575
• Wikipedia, Partition of a set

Crossrefs

Column p=7 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<8, [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, 7):
seq(a(n), n=7..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 8, {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, 7];
Table[a[n], {n, 7, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)