%I #5 Mar 03 2020 15:49:01

%S 1,21,166,1247,7855,47245,284968,1741235,10782872,69537976,471717130,

%T 3336898255,24584784957,189704257763,1530649634720,12849873769593,

%U 111945035887787,1011184665775833,9458811859041042,91480934118104305,913112230809837136,9391472034599656856

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

%H Alois P. Heinz, <a href="/A332944/b332944.txt">Table of n, a(n) for n = 4..576</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%p b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,

%p add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,

%p max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))

%p end:

%p a:= n-> b(n, 1, 4)[2]:

%p seq(a(n), n=4..25);

%Y Column k=4 of A319298.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Mar 03 2020