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A270494 Sum of the sizes of the second blocks in all set partitions of {1,2,...,n}.

%I A270494 #12 May 27 2018 02:00:26
%S A270494 1,5,21,88,387,1816,9123,48971,279855,1695902,10856879,73173016,
%T A270494 517597981,3831970709,29617983433,238460465120,1995828043987,
%U A270494 17333096360920,155936489571399,1451019052068763,13945778132786915,138259832617525950,1412263078623261399
%N A270494 Sum of the sizes of the second blocks in all set partitions of {1,2,...,n}.
%H A270494 Alois P. Heinz, <a href="/A270494/b270494.txt">Table of n, a(n) for n = 2..575</a>
%H A270494 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A270494 b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p A270494       add((p->`if`(j<3, [p[1], p[2]+p[1]*x^j], p))(
%p A270494        b(n-1, max(m, j))), j=1..m+1))
%p A270494     end:
%p A270494 a:= n-> coeff(b(n, 0)[2], x, 2):
%p A270494 seq(a(n), n=2..25);
%t A270494 b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 3, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n-1, Max[m, j]]], {j, 1, m + 1}]];
%t A270494 a[n_] := Coefficient[b[n, 0][[2]], x, 2];
%t A270494 Table[a[n], {n, 2, 25}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A270494 Column p=2 of A270236.
%K A270494 nonn
%O A270494 2,2
%A A270494 _Alois P. Heinz_, Mar 18 2016