A320760 Number of ordered set partitions of [n] where the maximal block size equals four.

1, 10, 120, 1540, 21490, 326970, 5402250, 96500250, 1855334250, 38228190000, 840776937000, 19666511865000, 487617137007000, 12776791730703000, 352825452012033000, 10242418813814187000, 311854958169459705000, 9937942309809373860000, 330821844137019184950000

Offset

4,2

Links

Alois P. Heinz, Table of n, a(n) for n = 4..424

Formula

E.g.f.: 1/(1-Sum_{i=1..4} x^i/i!) - 1/(1-Sum_{i=1..3} x^i/i!).

a(n) = A276924(n) - A189886(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))(4):
seq(a(n), n=4..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 = 4}, b[n, k] - b[n, k-1]];
a /@ Range[4, 25] (* Jean-François Alcover, Dec 14 2020, after Alois P. Heinz *)

Crossrefs

Column k=4 of A276922.

Cf. A189886, A276924.

Sequence in context: A005949 A027568 A318495 * A366711 A034255 A363310

Adjacent sequences: A320757 A320758 A320759 * A320761 A320762 A320763

Keyword

nonn

Author

Alois P. Heinz, Oct 20 2018

Status

approved