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A332946 Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

%I A332946 #5 Mar 03 2020 17:02:06
%S A332946 1,43,617,7681,79756,741665,6467891,54658254,451897330,3685879069,
%T A332946 30091146181,248749105815,2091117462980,17933165800591,
%U A332946 157654535847037,1426401197217090,13303368764700743,127934361462621048,1268098183967052868,12948542410221048226
%N A332946 Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H A332946 Alois P. Heinz, <a href="/A332946/b332946.txt">Table of n, a(n) for n = 6..576</a>
%H A332946 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A332946 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332946       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
%p A332946       max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332946     end:
%p A332946 a:= n-> b(n, 1, 6)[2]:
%p A332946 seq(a(n), n=6..25);
%Y A332946 Column k=6 of A319298.
%K A332946 nonn
%O A332946 6,2
%A A332946 _Alois P. Heinz_, Mar 03 2020