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A285367 Sum of the entries in the fifth blocks of all set partitions of [n].

%I A285367 #7 May 27 2018 08:27:12
%S A285367 5,96,1148,11122,96454,787959,6250696,49115820,387561065,3100950735,
%T A285367 25330467332,212222629466,1828990798243,16241051507536,
%U A285367 148696716804278,1403754413149792,13658941220426754,136899626339091133,1412247058871264298,14982353645545370808
%N A285367 Sum of the entries in the fifth blocks of all set partitions of [n].
%H A285367 Alois P. Heinz, <a href="/A285367/b285367.txt">Table of n, a(n) for n = 5..400</a>
%H A285367 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285367 a(n) = A285362(n,5).
%p A285367 a:= proc(h) option remember; local b; b:=
%p A285367       proc(n, m) option remember;
%p A285367         `if`(n=0, [1, 0], add((p-> `if`(j=5, p+ [0,
%p A285367         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285367       end: b(h, 0)[2]
%p A285367     end:
%p A285367 seq(a(n), n=5..30);
%t A285367 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 5, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285367 Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285367 Column k=5 of A285362.
%K A285367 nonn
%O A285367 5,1
%A A285367 _Alois P. Heinz_, Apr 17 2017