cp's OEIS Frontend

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

%I A272500 #4 May 01 2016 17:58:18
%S A272500 1,11,198,2860,47047,738738,12828816,223282488,4179020274,80464009340,
%T A272500 1640551617848,34682405557800,770529476530814,17782248154604934,
%U A272500 428864975324828328,10740325059575465640,279932748231053890830,7564798231253861700960,212075260563875086898520
%N A272500 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to ten.
%H A272500 Alois P. Heinz, <a href="/A272500/b272500.txt">Table of n, a(n) for n = 10..450</a>
%F A272500 E.g.f.: x^10 * Product_{i=1..10} (i-1)!/(i!-x^i).
%p A272500 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272500        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272500     end:
%p A272500 a:= n-> (k-> b(n, k) -b(n, k-1))(10):
%p A272500 seq(a(n), n=10..30);
%Y A272500 Column k=10 of A262071.
%K A272500 nonn
%O A272500 10,2
%A A272500 _Alois P. Heinz_, May 01 2016