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A333067 Number of entries in the tenth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

%I A333067 #5 Mar 06 2020 20:14:40
%S A333067 1,56,1772,41835,822277,14253254,225620777,3337585487,46894138343,
%T A333067 633327676249,8297945378872,106274752981884,1339352574256161,
%U A333067 16713308238007881,207742699406820799,2586686884152971976,32427925119758431591,410991858695177722552
%N A333067 Number of entries in the tenth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.
%H A333067 Alois P. Heinz, <a href="/A333067/b333067.txt">Table of n, a(n) for n = 10..576</a>
%H A333067 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A333067 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A333067       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
%p A333067        combinat[multinomial](n, i$j, n-i*j)/j!*
%p A333067       b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
%p A333067     end:
%p A333067 a:= n-> b(n$2, 10)[2]:
%p A333067 seq(a(n), n=10..27);
%Y A333067 Column k=10 of A319375.
%K A333067 nonn
%O A333067 10,2
%A A333067 _Alois P. Heinz_, Mar 06 2020