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A332945 Number of entries in the fifth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

%I A332945 #5 Mar 03 2020 16:48:50
%S A332945 1,31,337,3305,27085,203278,1470470,10525307,74735025,534251602,
%T A332945 3917281240,29620189877,230717097457,1858373700800,15544789470865,
%U A332945 135021858204377,1215283222207344,11317462847981403,108929278516177839,1082642589072326140,11099778977689173356
%N A332945 Number of entries in the fifth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H A332945 Alois P. Heinz, <a href="/A332945/b332945.txt">Table of n, a(n) for n = 5..576</a>
%H A332945 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A332945 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332945       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
%p A332945       max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332945     end:
%p A332945 a:= n-> b(n, 1, 5)[2]:
%p A332945 seq(a(n), n=5..25);
%Y A332945 Column k=5 of A319298.
%K A332945 nonn
%O A332945 5,2
%A A332945 _Alois P. Heinz_, Mar 03 2020