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%I #6 Mar 03 2020 21:49:51
%S 1,73,1666,31241,486377,6638568,82413787,961757669,10756109317,
%T 116409307679,1228840258412,12766418662681,131564790987337,
%U 1352403410824806,13925656629847559,144227711099572501,1508401366805906552,15986784485974156076,172225656206792090516
%N Number of entries in the eighth blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H Alois P. Heinz, <a href="/A332948/b332948.txt">Table of n, a(n) for n = 8..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, 8)[2]:
%p seq(a(n), n=8..26);
%Y Column k=8 of A319298.
%K nonn
%O 8,2
%A _Alois P. Heinz_, Mar 03 2020
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