%I #5 Mar 06 2020 19:40:56
%S 1,29,499,6676,77078,810470,8016373,76334142,713507667,6658565009,
%T 62882380589,606149817728,5983648334738,60440402586898,
%U 622934996801505,6532386995235676,69575530733726891,752420279343383619,8269751757387345271,92538014365261646366
%N Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.
%H Alois P. Heinz, <a href="/A333064/b333064.txt">Table of n, a(n) for n = 7..576</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
%p combinat[multinomial](n, i$j, n-i*j)/j!*
%p b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
%p end:
%p a:= n-> b(n$2, 7)[2]:
%p seq(a(n), n=7..26);
%Y Column k=7 of A319375.
%K nonn
%O 7,2
%A _Alois P. Heinz_, Mar 06 2020
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