cp's OEIS Frontend

A272497 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to seven.

%I A272497 #4 May 01 2016 17:46:16
%S A272497 1,8,108,1200,15510,194832,2749032,39402792,614555370,9964468800,
%T A272497 172686804576,3129181488576,60039964804248,1204868044448640,
%U A272497 25426155055055040,560350692475352064,12919636322380914984,310342487192287684992,7768115419959585662400
%N A272497 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to seven.
%H A272497 Alois P. Heinz, <a href="/A272497/b272497.txt">Table of n, a(n) for n = 7..450</a>
%F A272497 E.g.f.: x^7 * Product_{i=1..7} (i-1)!/(i!-x^i).
%p A272497 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272497        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272497     end:
%p A272497 a:= n-> (k-> b(n, k) -b(n, k-1))(7):
%p A272497 seq(a(n), n=7..30);
%Y A272497 Column k=7 of A262071.
%K A272497 nonn
%O A272497 7,2
%A A272497 _Alois P. Heinz_, May 01 2016