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A333063 Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.

%I A333063 #5 Mar 06 2020 19:26:08
%S A333063 1,22,295,3145,29503,256565,2144517,17743090,148599335,1276302900,
%T A333063 11282648837,102385155537,949462521827,8967298797097,86161326118467,
%U A333063 843025151446964,8418457337349711,86033922399717781,902026616406147607,9718711403938257151
%N A333063 Number of entries in the sixth blocks of all set partitions of [n] when blocks are ordered by decreasing lengths.
%H A333063 Alois P. Heinz, <a href="/A333063/b333063.txt">Table of n, a(n) for n = 6..576</a>
%H A333063 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A333063 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i<1, 0,
%p A333063       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(
%p A333063        combinat[multinomial](n, i$j, n-i*j)/j!*
%p A333063       b(n-i*j, min(n-i*j, i-1), max(0, t-j))), j=0..n/i)))
%p A333063     end:
%p A333063 a:= n-> b(n$2, 6)[2]:
%p A333063 seq(a(n), n=6..25);
%Y A333063 Column k=6 of A319375.
%K A333063 nonn
%O A333063 6,2
%A A333063 _Alois P. Heinz_, Mar 06 2020