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A270763 Total sum of the sizes of all blocks with maximal element 9 in all set partitions of {1,2,...,n}.

%I A270763 #8 May 26 2018 11:20:13
%S A270763 54267,230884,1090335,5624233,31336468,187018111,1187718179,
%T A270763 7984210898,56562256041,420709044049,3275003008250,26608043757997,
%U A270763 225076163325759,1977999456151260,18024710156370739,170022295940977197,1657528265315075476,16676976427179730819
%N A270763 Total sum of the sizes of all blocks with maximal element 9 in all set partitions of {1,2,...,n}.
%H A270763 Alois P. Heinz, <a href="/A270763/b270763.txt">Table of n, a(n) for n = 9..577</a>
%H A270763 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t A270763 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 A270763 a[n_] := b[n, 0, Max[0, 1 + n - 9]][[2]];
%t A270763 Array[a, 24, 9] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
%Y A270763 Column k=9 of A270701.
%Y A270763 A diagonal of A270702.
%K A270763 nonn
%O A270763 9,1
%A A270763 _Alois P. Heinz_, Mar 22 2016