A270496 Sum of the sizes of the fourth blocks in all set partitions of {1,2,...,n}.

1, 12, 97, 675, 4418, 28396, 183615, 1211936, 8237223, 57944187, 422950882, 3206531728, 25247250641, 206313943476, 1747990803645, 15336960025775, 139187730958406, 1304967471569208, 12624893940830455, 125892638744630088, 1292581981392588771

Offset: 4

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..575
• Wikipedia, Partition of a set

Crossrefs

Column p=4 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<5, [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, 4):
seq(a(n), n=4..30);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 5, {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, 4];
Table[a[n], {n, 4, 30}] (* Jean-François Alcover, May 27 2018, translated from Maple *)