|
%I #8 May 26 2018 11:20:31
%S 30,67,195,670,2623,11437,54692,283625,1581303,9413380,59497049,
%T 397402597,2794008798,20606565063,158955946879,1279119138486,
%U 10712907438835,93190762200361,840437752639132,7844783028326405,75673025264120531,753330825335964276
%N Total sum of the sizes of all blocks with maximal element 4 in all set partitions of {1,2,...,n}.
%H Alois P. Heinz, <a href="/A270758/b270758.txt">Table of n, a(n) for n = 4..577</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%t 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 a[n_] := b[n, 0, Max[0, 1 + n - 4]][[2]];
%t Array[a, 24, 4] (* _Jean-François Alcover_, May 26 2018, from Maple code for A270701 *)
%Y Column k=4 of A270701.
%Y A diagonal of A270702.
%K nonn
%O 4,1
%A _Alois P. Heinz_, Mar 22 2016
|
