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A270498 Sum of the sizes of the sixth blocks in all set partitions of {1,2,...,n}.

%I A270498 #10 May 27 2018 02:29:07
%S A270498 1,23,324,3645,36223,334751,2965654,25691104,220643295,1897548384,
%T A270498 16463907354,144927422746,1299763249771,11912250951457,
%U A270498 111803042249042,1076045623549383,10628068291940557,107760039986995689,1121581530251066296,11980190581723881858
%N A270498 Sum of the sizes of the sixth blocks in all set partitions of {1,2,...,n}.
%H A270498 Alois P. Heinz, <a href="/A270498/b270498.txt">Table of n, a(n) for n = 6..575</a>
%H A270498 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A270498 b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p A270498       add((p->`if`(j<7, [p[1], p[2]+p[1]*x^j], p))(
%p A270498        b(n-1, max(m, j))), j=1..m+1))
%p A270498     end:
%p A270498 a:= n-> coeff(b(n, 0)[2], x, 6):
%p A270498 seq(a(n), n=6..30);
%t A270498 b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 7, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
%t A270498 a[n_] := Coefficient[b[n, 0][[2]], x, 6];
%t A270498 Table[a[n], {n, 6, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A270498 Column p=6 of A270236.
%K A270498 nonn
%O A270498 6,2
%A A270498 _Alois P. Heinz_, Mar 18 2016