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Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to eight.
2

%I #4 May 01 2016 17:49:17

%S 1,9,135,1650,23265,316602,4810806,73880235,1229123610,21174714990,

%T 388551217626,7431930745668,150102842702670,3162843042018660,

%U 69923464752835980,1611044465380180974,38759812951913315262,969843174518264324850,25246982138722170061950

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

%H Alois P. Heinz, <a href="/A272498/b272498.txt">Table of n, a(n) for n = 8..450</a>

%F E.g.f.: x^8 * Product_{i=1..8} (i-1)!/(i!-x^i).

%p b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,

%p b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))

%p end:

%p a:= n-> (k-> b(n, k) -b(n, k-1))(8):

%p seq(a(n), n=8..30);

%Y Column k=8 of A262071.

%K nonn

%O 8,2

%A _Alois P. Heinz_, May 01 2016