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

Author

Alois P. Heinz, Oct 20 2018

Keywords

• nonn

Links

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

Crossrefs

Column k=4 of A276922.

Cf. A189886, A276924.

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))(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 *)

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).