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A270760 Total sum of the sizes of all blocks with maximal element 6 in all set partitions of {1,2,...,n}.

%I A270760 #8 May 26 2018 11:20:23
%S A270760 463,1429,5204,21485,98367,492112,2661473,15433189,95330022,623920659,
%T A270760 4307488855,31251896082,237507413011,1885386460081,15594381406204,
%U A270760 134098780567817,1196511239506523,11057997444651072,105684135069638365,1043003293054453121
%N A270760 Total sum of the sizes of all blocks with maximal element 6 in all set partitions of {1,2,...,n}.
%H A270760 Alois P. Heinz, <a href="/A270760/b270760.txt">Table of n, a(n) for n = 6..577</a>
%H A270760 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t A270760 b[n_, m_, t_] := b[n, m, t] = If[n == 0, {1, 0}, Sum[If[t == 1 && j != m + 1, 0, Function[p, p + If[j == -t || t == 1 && j == m + 1, {0, p[[1]]}, 0]][b[n - 1, Max[m, j], If[t == 1 && j == m + 1, -j, If[t < 0, t, If[t > 0, t - 1, 0]]]]]], {j, 1, m + 1}]];
%t A270760 a[n_] := b[n, 0, Max[0, 1 + n - 6]][[2]];
%t A270760 Array[a, 24, 6] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
%Y A270760 Column k=6 of A270701.
%Y A270760 A diagonal of A270702.
%K A270760 nonn
%O A270760 6,1
%A A270760 _Alois P. Heinz_, Mar 22 2016