A272495 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to five.

1, 6, 63, 560, 5922, 61992, 739662, 9086616, 122792670, 1741884144, 26631631026, 428931318816, 7362963616008, 132977285400960, 2538822785931432, 50863863365419104, 1070731366348427784, 23576426902769412672, 542918591829347774040, 13035693339696004705728

Offset

5,2

Links

Alois P. Heinz, Table of n, a(n) for n = 5..450

Formula

E.g.f.: x^5 * Product_{i=1..5} (i-1)!/(i!-x^i).

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))(5):
seq(a(n), n=5..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, 5] - b[n, 4];
a /@ Range[5, 30] (* Jean-François Alcover, Dec 11 2020, after Alois P. Heinz *)

Crossrefs

Column k=5 of A262071.

Sequence in context: A267248 A053535 A268220 * A039937 A134112 A071588

Adjacent sequences: A272492 A272493 A272494 * A272496 A272497 A272498

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved