A270494 Sum of the sizes of the second blocks in all set partitions of {1,2,...,n}.

1, 5, 21, 88, 387, 1816, 9123, 48971, 279855, 1695902, 10856879, 73173016, 517597981, 3831970709, 29617983433, 238460465120, 1995828043987, 17333096360920, 155936489571399, 1451019052068763, 13945778132786915, 138259832617525950, 1412263078623261399

Offset: 2

Author

Alois P. Heinz, Mar 18 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..575
• Wikipedia, Partition of a set

Crossrefs

Column p=2 of A270236.

Programs

Maple

b:= proc(n, m) option remember; `if`(n=0, [1, 0],
      add((p->`if`(j<3, [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, 2):
seq(a(n), n=2..25);

Mathematica

b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 3, {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, 2];
Table[a[n], {n, 2, 25}] (* Jean-François Alcover, May 27 2018, translated from Maple *)