A320758 Number of ordered set partitions of [n] where the maximal block size equals two.

1, 6, 42, 330, 2970, 30240, 345240, 4377240, 61122600, 933055200, 15470254800, 277005128400, 5329454130000, 109681187616000, 2404894892400000, 55977698400624000, 1378748676601296000, 35829233832135744000, 979763376201049440000, 28124715476056399200000

Offset: 2

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 2..428

Crossrefs

Column k=2 of A276922.

Cf. A000142, A080599.

Programs

Maple

b:= proc(n, k) option remember; `if`(n=0, 1, add(
      b(n-i, k)*binomial(n, i), i=1..min(n, k)))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(2):
seq(a(n), n=2..25);

Mathematica

b[n_, k_] := b[n, k] = If[n == 0, 1, Sum[b[n - i, k] Binomial[n, i], {i, 1, Min[n, k]}]];
a[n_] := With[{k = 2}, b[n, k] - b[n, k-1]];
a /@ Range[2, 25] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Formula

E.g.f.: 1/(1-Sum_{i=1..2} x^i/i!) - 1/(1-x).

A(n) = A080599(n) - A000142(n).