A272499 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to nine.

1, 10, 165, 2200, 33605, 492492, 8018010, 131342640, 2321677930, 42349478600, 820275716546, 16515429370440, 350240612952230, 7731410818511380, 178693701272340540, 4296129057927296304, 107666415418378051950, 2801776425029317564400, 75741144900761549630850

Offset

9,2

Links

Alois P. Heinz, Table of n, a(n) for n = 9..450

Formula

E.g.f.: x^9 * Product_{i=1..9} (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))(9):
seq(a(n), n=9..30);

Crossrefs

Column k=9 of A262071.

Sequence in context: A064747 A285995 A278096 * A305604 A367444 A054688

Adjacent sequences: A272496 A272497 A272498 * A272500 A272501 A272502

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved