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

%I A272499 #4 May 01 2016 17:52:10
%S A272499 1,10,165,2200,33605,492492,8018010,131342640,2321677930,42349478600,
%T A272499 820275716546,16515429370440,350240612952230,7731410818511380,
%U A272499 178693701272340540,4296129057927296304,107666415418378051950,2801776425029317564400,75741144900761549630850
%N A272499 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to nine.
%H A272499 Alois P. Heinz, <a href="/A272499/b272499.txt">Table of n, a(n) for n = 9..450</a>
%F A272499 E.g.f.: x^9 * Product_{i=1..9} (i-1)!/(i!-x^i).
%p A272499 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272499        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272499     end:
%p A272499 a:= n-> (k-> b(n, k) -b(n, k-1))(9):
%p A272499 seq(a(n), n=9..30);
%Y A272499 Column k=9 of A262071.
%K A272499 nonn
%O A272499 9,2
%A A272499 _Alois P. Heinz_, May 01 2016