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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}. 3

%I

%S 10279,39848,174029,838485,4395802,24825947,149888167,961547874,

%T 6521484087,46567171489,348842020704,2733150610201,22336983535651,

%U 189972322541416,1677852685522313,15360428047484945,145515022547392842,1424312554941600127,14384441797357797779

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

%H Alois P. Heinz, <a href="/A270762/b270762.txt">Table of n, a(n) for n = 8..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 - 8]][[2]];

%t Array[a, 24, 8] (* Jean-Fran├žois Alcover, May 26 2018, from Maple code for A270701 *)

%Y Column k=8 of A270701.

%Y A diagonal of A270702.

%K nonn

%O 8,1

%A _Alois P. Heinz_, Mar 22 2016

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Last modified October 16 15:08 EDT 2021. Contains 348042 sequences. (Running on oeis4.)