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A333066 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

%I A333066 #5 Mar 06 2020 20:04:46
%S A333066 1,46,1211,24047,401337,5957407,81381744,1046405027,12866407790,
%T A333066 153103993523,1780561219354,20417258320972,232758457316938,
%U A333066 2658399095977056,30621521649045981,357523836553565584,4243836001737759231,51265500225372571466,629904897694885693327
%N A333066 Number of entries in the ninth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.
%H A333066 Alois P. Heinz, <a href="/A333066/b333066.txt">Table of n, a(n) for n = 9..576</a>
%H A333066 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A333066 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A333066       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
%p A333066        combinat[multinomial](n, i$j, n-i*j)/j!*
%p A333066       b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
%p A333066     end:
%p A333066 a:= n-> b(n$2, 9)[2]:
%p A333066 seq(a(n), n=9..27);
%Y A333066 Column k=9 of A319375.
%K A333066 nonn
%O A333066 9,2
%A A333066 _Alois P. Heinz_, Mar 06 2020