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A270761 Total sum of the sizes of all blocks with maximal element 7 in all set partitions of {1,2,...,n}.

%I A270761 #8 May 26 2018 11:20:20
%S A270761 2095,7307,29278,131007,643401,3426532,19610565,119762455,776018428,
%T A270761 5310053713,38218929257,288361428110,2274040468083,18695782169431,
%U A270761 159876844021430,1419201089763907,13053572286094533,124202259586825404,1220668798203165121
%N A270761 Total sum of the sizes of all blocks with maximal element 7 in all set partitions of {1,2,...,n}.
%H A270761 Alois P. Heinz, <a href="/A270761/b270761.txt">Table of n, a(n) for n = 7..577</a>
%H A270761 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t A270761 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 A270761 a[n_] := b[n, 0, Max[0, 1 + n - 7]][[2]];
%t A270761 Array[a, 24, 7] (* Jean-François Alcover, May 26 2018, from Maple code for A270701 *)
%Y A270761 Column k=7 of A270701.
%Y A270761 A diagonal of A270702.
%K A270761 nonn
%O A270761 7,1
%A A270761 _Alois P. Heinz_, Mar 22 2016