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A285369 Sum of the entries in the seventh blocks of all set partitions of [n].

%I A285369 #12 May 27 2018 10:31:48
%S A285369 7,232,4518,67898,875365,10228471,111964040,1173487986,11959590504,
%T A285369 119889568676,1192711559418,11859084564254,118526150123309,
%U A285369 1196311505171568,12239696866561282,127315711586330538,1349476206629576995,14599608027440148129,161399084259928978190
%N A285369 Sum of the entries in the seventh blocks of all set partitions of [n].
%H A285369 Alois P. Heinz, <a href="/A285369/b285369.txt">Table of n, a(n) for n = 7..400</a>
%H A285369 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285369 a(n) = A285362(n,7).
%p A285369 a:= proc(h) option remember; local b; b:=
%p A285369       proc(n, m) option remember;
%p A285369         `if`(n=0, [1, 0], add((p-> `if`(j=7, p+ [0,
%p A285369         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285369       end: b(h, 0)[2]
%p A285369     end:
%p A285369 seq(a(n), n=7..30);
%t A285369 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 7, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285369 Table[a[n], {n, 7, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285369 Column k=7 of A285362.
%K A285369 nonn
%O A285369 7,1
%A A285369 _Alois P. Heinz_, Apr 17 2017