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A285364 Sum of the entries in the second blocks of all set partitions of [n].

%I A285364 #10 May 27 2018 11:02:01
%S A285364 2,12,58,273,1329,6839,37423,217606,1340597,8719806,59680387,
%T A285364 428481322,3218109788,25220647760,205790862332,1744755841379,
%U A285364 15342274425585,139692065365753,1314995731359189,12780466391685166,128081591768679823,1322011886920066940
%N A285364 Sum of the entries in the second blocks of all set partitions of [n].
%H A285364 Alois P. Heinz, <a href="/A285364/b285364.txt">Table of n, a(n) for n = 2..575</a>
%H A285364 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285364 a(n) = A285362(n,2).
%e A285364 a(3) = 12 because the sum of the entries in the second blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+3+2+5+2 = 12.
%p A285364 a:= proc(h) option remember; local b; b:=
%p A285364       proc(n, m) option remember;
%p A285364         `if`(n=0, [1, 0], add((p-> `if`(j=2, p+ [0,
%p A285364         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285364       end: b(h, 0)[2]
%p A285364     end:
%p A285364 seq(a(n), n=2..30);
%t A285364 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 2, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285364 Table[a[n], {n, 2, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285364 Column k=2 of A285362.
%K A285364 nonn
%O A285364 2,1
%A A285364 _Alois P. Heinz_, Apr 17 2017