A320761 Number of ordered set partitions of [n] where the maximal block size equals five.

1, 12, 168, 2464, 38808, 657972, 11997216, 234594360, 4903616718, 109205019924, 2582909885556, 64686057980544, 1710536977653504, 47637803779229664, 1393903719674129664, 42758329987344875904, 1372254504736418142840, 45989719374155059863360

Offset: 5

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..424

Crossrefs

Column k=5 of A276922.

Cf. A276924, A276925.

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))(5):
seq(a(n), n=5..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 = 5}, b[n, k] - b[n, k-1]];
a /@ Range[5, 25] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Formula

E.g.f.: 1/(1-Sum_{i=1..5} x^i/i!) - 1/(1-Sum_{i=1..4} x^i/i!).

a(n) = A276925(n) - A276924(n).