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A272497 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to seven. 2

%I

%S 1,8,108,1200,15510,194832,2749032,39402792,614555370,9964468800,

%T 172686804576,3129181488576,60039964804248,1204868044448640,

%U 25426155055055040,560350692475352064,12919636322380914984,310342487192287684992,7768115419959585662400

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

%H Alois P. Heinz, <a href="/A272497/b272497.txt">Table of n, a(n) for n = 7..450</a>

%F E.g.f.: x^7 * Product_{i=1..7} (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))(7):

%p seq(a(n), n=7..30);

%Y Column k=7 of A262071.

%K nonn

%O 7,2

%A _Alois P. Heinz_, May 01 2016

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Last modified September 25 04:57 EDT 2022. Contains 356953 sequences. (Running on oeis4.)