A272494 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to four.

1, 5, 45, 350, 3290, 30870, 334950, 3765300, 46950750, 617867250, 8815156350, 133031398500, 2149039893000, 36645888279000, 662781093975000, 12612741639498000, 252857867367105000, 5314211504296695000, 117053051989758885000, 2693288170000578150000

Offset: 4

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..450

Crossrefs

Column k=4 of A262071.

Programs

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
       b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
    end:
a:= n-> (k-> b(n, k) -b(n, k-1))(4):
seq(a(n), n=4..30);

Mathematica

b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, b[n, i - 1] + If[i > n, 0, Binomial[n, i]*b[n - i, i]]]];
a[n_] := b[n, 4] - b[n, 3];
a /@ Range[4, 30] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Formula

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