%I #5 Mar 06 2020 20:14:40

%S 1,56,1772,41835,822277,14253254,225620777,3337585487,46894138343,

%T 633327676249,8297945378872,106274752981884,1339352574256161,

%U 16713308238007881,207742699406820799,2586686884152971976,32427925119758431591,410991858695177722552

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

%H Alois P. Heinz, <a href="/A333067/b333067.txt">Table of n, a(n) for n = 10..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, 10)[2]:

%p seq(a(n), n=10..27);

%Y Column k=10 of A319375.

%K nonn

%O 10,2

%A _Alois P. Heinz_, Mar 06 2020