A272500 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to ten.

1, 11, 198, 2860, 47047, 738738, 12828816, 223282488, 4179020274, 80464009340, 1640551617848, 34682405557800, 770529476530814, 17782248154604934, 428864975324828328, 10740325059575465640, 279932748231053890830, 7564798231253861700960, 212075260563875086898520

Offset

10,2

Links

Alois P. Heinz, Table of n, a(n) for n = 10..450

Formula

E.g.f.: x^10 * Product_{i=1..10} (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))(10):
seq(a(n), n=10..30);

Crossrefs

Column k=10 of A262071.

Sequence in context: A186251 A234628 A105124 * A034831 A142362 A140534

Adjacent sequences: A272497 A272498 A272499 * A272501 A272502 A272503

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved