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A332947 Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by increasing lengths.

%I A332947 #5 Mar 03 2020 20:16:39
%S A332947 1,57,1045,16126,207131,2351933,24592218,244969609,2361155669,
%T A332947 22194089013,205472269667,1894376413748,17523281149447,
%U A332947 163348288354057,1541060427442896,14781379209476531,144692817107094283,1449416720608086968,14882752251954912426
%N A332947 Number of entries in the seventh blocks of all set partitions of [n] when blocks are ordered by increasing lengths.
%H A332947 Alois P. Heinz, <a href="/A332947/b332947.txt">Table of n, a(n) for n = 7..576</a>
%H A332947 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A332947 b:= proc(n, i, t) option remember; `if`(n=0, [1, 0], `if`(i>n, 0,
%p A332947       add((p-> p+`if`(t>0 and t-j<1, [0, p[1]*i], 0))(b(n-i*j, i+1,
%p A332947       max(0, t-j))/j!*combinat[multinomial](n, i$j, n-i*j)), j=0..n/i)))
%p A332947     end:
%p A332947 a:= n-> b(n, 1, 7)[2]:
%p A332947 seq(a(n), n=7..25);
%Y A332947 Column k=7 of A319298.
%K A332947 nonn
%O A332947 7,2
%A A332947 _Alois P. Heinz_, Mar 03 2020