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A270499 Sum of the sizes of the seventh blocks in all set partitions of {1,2,...,n}.

%I A270499 #10 May 27 2018 02:29:15
%S A270499 1,30,536,7473,90223,995191,10354804,103779309,1016654053,9840330258,
%T A270499 94884791378,917358452410,8938608738199,88139900141632,
%U A270499 882388425916186,8991438542446875,93434278760386701,991477889069432577,10753621593467498170,119276548511953973463
%N A270499 Sum of the sizes of the seventh blocks in all set partitions of {1,2,...,n}.
%H A270499 Alois P. Heinz, <a href="/A270499/b270499.txt">Table of n, a(n) for n = 7..575</a>
%H A270499 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A270499 b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p A270499       add((p->`if`(j<8, [p[1], p[2]+p[1]*x^j], p))(
%p A270499        b(n-1, max(m, j))), j=1..m+1))
%p A270499     end:
%p A270499 a:= n-> coeff(b(n, 0)[2], x, 7):
%p A270499 seq(a(n), n=7..30);
%t A270499 b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 8, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
%t A270499 a[n_] := Coefficient[b[n, 0][[2]], x, 7];
%t A270499 Table[a[n], {n, 7, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A270499 Column p=7 of A270236.
%K A270499 nonn
%O A270499 7,2
%A A270499 _Alois P. Heinz_, Mar 18 2016