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A270762 Total sum of the sizes of all blocks with maximal element 8 in all set partitions of {1,2,...,n}.

%I A270762 #8 May 26 2018 11:20:16
%S A270762 10279,39848,174029,838485,4395802,24825947,149888167,961547874,
%T A270762 6521484087,46567171489,348842020704,2733150610201,22336983535651,
%U A270762 189972322541416,1677852685522313,15360428047484945,145515022547392842,1424312554941600127,14384441797357797779
%N A270762 Total sum of the sizes of all blocks with maximal element 8 in all set partitions of {1,2,...,n}.
%H A270762 Alois P. Heinz, <a href="/A270762/b270762.txt">Table of n, a(n) for n = 8..577</a>
%H A270762 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t A270762 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 A270762 a[n_] := b[n, 0, Max[0, 1 + n - 8]][[2]];
%t A270762 Array[a, 24, 8] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
%Y A270762 Column k=8 of A270701.
%Y A270762 A diagonal of A270702.
%K A270762 nonn
%O A270762 8,1
%A A270762 _Alois P. Heinz_, Mar 22 2016