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A285368 Sum of the entries in the sixth blocks of all set partitions of [n].

%I A285368 #8 May 27 2018 08:27:29
%S A285368 6,154,2380,28975,308127,3018824,28133574,254715640,2274064881,
%T A285368 20242054046,181155397430,1640541610028,15107388580258,
%U A285368 141982420633882,1365335004650614,13456694682282849,136069364339492065,1412201447170038064,15044059353340996950
%N A285368 Sum of the entries in the sixth blocks of all set partitions of [n].
%H A285368 Alois P. Heinz, <a href="/A285368/b285368.txt">Table of n, a(n) for n = 6..400</a>
%H A285368 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285368 a(n) = A285362(n,6).
%p A285368 a:= proc(h) option remember; local b; b:=
%p A285368       proc(n, m) option remember;
%p A285368         `if`(n=0, [1, 0], add((p-> `if`(j=6, p+ [0,
%p A285368         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285368       end: b(h, 0)[2]
%p A285368     end:
%p A285368 seq(a(n), n=6..30);
%t A285368 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 6, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285368 Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285368 Column k=6 of A285362.
%K A285368 nonn
%O A285368 6,1
%A A285368 _Alois P. Heinz_, Apr 17 2017