cp's OEIS Frontend

A272498 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to eight.

%I A272498 #4 May 01 2016 17:49:17
%S A272498 1,9,135,1650,23265,316602,4810806,73880235,1229123610,21174714990,
%T A272498 388551217626,7431930745668,150102842702670,3162843042018660,
%U A272498 69923464752835980,1611044465380180974,38759812951913315262,969843174518264324850,25246982138722170061950
%N A272498 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to eight.
%H A272498 Alois P. Heinz, <a href="/A272498/b272498.txt">Table of n, a(n) for n = 8..450</a>
%F A272498 E.g.f.: x^8 * Product_{i=1..8} (i-1)!/(i!-x^i).
%p A272498 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272498        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272498     end:
%p A272498 a:= n-> (k-> b(n, k) -b(n, k-1))(8):
%p A272498 seq(a(n), n=8..30);
%Y A272498 Column k=8 of A262071.
%K A272498 nonn
%O A272498 8,2
%A A272498 _Alois P. Heinz_, May 01 2016