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A270759 Total sum of the sizes of all blocks with maximal element 5 in all set partitions of {1,2,...,n}.

%I A270759 #8 May 26 2018 11:20:27
%S A270759 112,299,979,3702,15717,73561,374718,2057641,12088759,75528808,
%T A270759 499336559,3478563389,25443377280,194791872127,1556720156567,
%U A270759 12955521377878,112041717014289,1004979994978317,9333443375249734,89610138696275685,888152337277216747
%N A270759 Total sum of the sizes of all blocks with maximal element 5 in all set partitions of {1,2,...,n}.
%H A270759 Alois P. Heinz, <a href="/A270759/b270759.txt">Table of n, a(n) for n = 5..577</a>
%H A270759 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t A270759 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 A270759 a[n_] := b[n, 0, Max[0, 1 + n - 5]][[2]];
%t A270759 Array[a, 24, 5] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
%Y A270759 Column k=5 of A270701.
%Y A270759 A diagonal of A270702.
%K A270759 nonn
%O A270759 5,1
%A A270759 _Alois P. Heinz_, Mar 22 2016