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A333065 Number of entries in the eighth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

%I A333065 #5 Mar 06 2020 19:50:44
%S A333065 1,37,796,13091,183074,2300949,26869727,298009584,3190196105,
%T A333065 33408754043,346447486658,3596858467639,37729664292626,
%U A333065 402420037089997,4378064125023471,48598561597491856,549602546782048959,6318831653757436761,73723789208978689966
%N A333065 Number of entries in the eighth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.
%H A333065 Alois P. Heinz, <a href="/A333065/b333065.txt">Table of n, a(n) for n = 8..576</a>
%H A333065 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A333065 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A333065       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
%p A333065        combinat[multinomial](n, i$j, n-i*j)/j!*
%p A333065       b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
%p A333065     end:
%p A333065 a:= n-> b(n$2, 8)[2]:
%p A333065 seq(a(n), n=8..26);
%Y A333065 Column k=8 of A319375.
%K A333065 nonn
%O A333065 8,2
%A A333065 _Alois P. Heinz_, Mar 06 2020