%I
%S 1,43,617,7681,79756,741665,6467891,54658254,451897330,3685879069,
%T 30091146181,248749105815,2091117462980,17933165800591,
%U 157654535847037,1426401197217090,13303368764700743,127934361462621048,1268098183967052868,12948542410221048226
%N Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H Alois P. Heinz, <a href="/A332946/b332946.txt">Table of n, a(n) for n = 6..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>n, 0,
%p add((p> p+`if`(t>0 and tj<1, [0, p[1]*i], 0))(b(ni*j, i+1,
%p max(0, tj))/j!*combinat[multinomial](n, i$j, ni*j)), j=0..n/i)))
%p end:
%p a:= n> b(n, 1, 6)[2]:
%p seq(a(n), n=6..25);
%Y Column k=6 of A319298.
%K nonn
%O 6,2
%A _Alois P. Heinz_, Mar 03 2020
