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A332944 Number of entries in the fourth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

%I A332944 #5 Mar 03 2020 15:49:01
%S A332944 1,21,166,1247,7855,47245,284968,1741235,10782872,69537976,471717130,
%T A332944 3336898255,24584784957,189704257763,1530649634720,12849873769593,
%U A332944 111945035887787,1011184665775833,9458811859041042,91480934118104305,913112230809837136,9391472034599656856
%N A332944 Number of entries in the fourth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H A332944 Alois P. Heinz, <a href="/A332944/b332944.txt">Table of n, a(n) for n = 4..576</a>
%H A332944 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A332944 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332944       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
%p A332944       max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332944     end:
%p A332944 a:= n-> b(n, 1, 4)[2]:
%p A332944 seq(a(n), n=4..25);
%Y A332944 Column k=4 of A319298.
%K A332944 nonn
%O A332944 4,2
%A A332944 _Alois P. Heinz_, Mar 03 2020