A320759 Number of ordered set partitions of [n] where the maximal block size equals three.

1, 8, 80, 860, 10290, 136080, 1977360, 31365600, 539847000, 10026139200, 199937337600, 4262167509600, 96744738090000, 2329950823200000, 59348032327584000, 1594257675506496000, 45047749044458160000, 1335740755933584000000, 41473196779273459200000

Offset

3,2

Links

Alois P. Heinz, Table of n, a(n) for n = 3..424

Formula

E.g.f.: 1/(1-Sum_{i=1..3} x^i/i!) - 1/(1-Sum_{i=1..2} x^i/i!).

a(n) = A189886(n) - A080599(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))(3):
seq(a(n), n=3..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 = 3}, b[n, k] - b[n, k-1]];
a /@ Range[3, 25] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Crossrefs

Column k=3 of A276922.

Cf. A080599, A189886.

Sequence in context: A346178 A102592 A345081 * A233123 A269796 A328128

Adjacent sequences: A320756 A320757 A320758 * A320760 A320761 A320762

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved