cp's OEIS Frontend

A272496 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to six.

%I A272496 #4 May 01 2016 17:41:48
%S A272496 1,7,84,840,9870,113652,1480248,19699680,286768482,4358914560,
%T A272496 71096721696,1216711960464,22116370171896,421629228820800,
%U A272496 8473857766133760,178260053918650704,3931319749640138856,90499126549555707984,2174651142277047610176,54390059451824183287200
%N A272496 Number of ordered set partitions of [n] with nondecreasing block sizes and maximal block size equal to six.
%H A272496 Alois P. Heinz, <a href="/A272496/b272496.txt">Table of n, a(n) for n = 6..450</a>
%F A272496 E.g.f.: x^6 * Product_{i=1..6} (i-1)!/(i!-x^i).
%p A272496 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A272496        b(n, i-1)+`if`(i>n, 0, binomial(n, i)*b(n-i, i))))
%p A272496     end:
%p A272496 a:= n-> (k-> b(n, k) -b(n, k-1))(6):
%p A272496 seq(a(n), n=6..30);
%Y A272496 Column k=6 of A262071.
%K A272496 nonn
%O A272496 6,2
%A A272496 _Alois P. Heinz_, May 01 2016