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

5,2

Links

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

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).

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 *)

Crossrefs

Column k=5 of A276922.

Cf. A276924, A276925.

Sequence in context: A182606 A079679 A216702 * A282045 A304960 A113380

Adjacent sequences: A320758 A320759 A320760 * A320762 A320763 A320764

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved