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A285366 Sum of the entries in the fourth blocks of all set partitions of [n].

%I A285366 #9 May 27 2018 08:10:43
%S A285366 4,55,495,3757,26421,180482,1230737,8520912,60531347,444006008,
%T A285366 3374292280,26605751388,217686862402,1847108846441,16237616979723,
%U A285366 147709622593855,1388722474550671,13477574785475778,134861358322272607,1389822348657508142,14735739124218384875
%N A285366 Sum of the entries in the fourth blocks of all set partitions of [n].
%H A285366 Alois P. Heinz, <a href="/A285366/b285366.txt">Table of n, a(n) for n = 4..400</a>
%H A285366 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285366 a(n) = A285362(n,4).
%p A285366 a:= proc(h) option remember; local b; b:=
%p A285366       proc(n, m) option remember;
%p A285366         `if`(n=0, [1, 0], add((p-> `if`(j=4, p+ [0,
%p A285366         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285366       end: b(h, 0)[2]
%p A285366     end:
%p A285366 seq(a(n), n=4..30);
%t A285366 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 4, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285366 Table[a[n], {n, 4, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285366 Column k=4 of A285362.
%K A285366 nonn
%O A285366 4,1
%A A285366 _Alois P. Heinz_, Apr 17 2017