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A270497 Sum of the sizes of the fifth blocks in all set partitions of {1,2,...,n}.

%I A270497 #10 May 27 2018 02:29:00
%S A270497 1,17,184,1641,13276,102244,770989,5795889,43967302,339403001,
%T A270497 2681449074,21763977864,181900742989,1567473197429,13932812925824,
%U A270497 127738400615689,1207445992487256,11759938209394472,117926100082535985,1216563820893322317,12901060857158377838
%N A270497 Sum of the sizes of the fifth blocks in all set partitions of {1,2,...,n}.
%H A270497 Alois P. Heinz, <a href="/A270497/b270497.txt">Table of n, a(n) for n = 5..575</a>
%H A270497 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A270497 b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p A270497       add((p->`if`(j<6, [p[1], p[2]+p[1]*x^j], p))(
%p A270497        b(n-1, max(m, j))), j=1..m+1))
%p A270497     end:
%p A270497 a:= n-> coeff(b(n, 0)[2], x, 5):
%p A270497 seq(a(n), n=5..30);
%t A270497 b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 6, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
%t A270497 a[n_] := Coefficient[b[n, 0][[2]], x, 5];
%t A270497 Table[a[n], {n, 5, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A270497 Column p=5 of A270236.
%K A270497 nonn
%O A270497 5,2
%A A270497 _Alois P. Heinz_, Mar 18 2016