A270502 Sum of the sizes of the tenth blocks in all set partitions of {1,2,...,n}.

1, 57, 1839, 44346, 891892, 15848311, 257647088, 3921554995, 56796169899, 792102157717, 10734723141617, 142380931674179, 1858965371935248, 24006134113802346, 307860388231938976, 3934302726222970593, 50254089923100713719, 643301179860716506788

Offset: 10

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..575
• Wikipedia, Partition of a set

Crossrefs

Column p=10 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<11, [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, 10):
seq(a(n), n=10..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 11, {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, 10];
Table[a[n], {n, 10, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)