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A285371 Sum of the entries in the ninth blocks of all set partitions of [n].

%I A285371 #7 May 27 2018 08:08:59
%S A285371 9,460,13365,291312,5313419,85887795,1273861815,17739276489,
%T A285371 235727269842,3025136223480,37838768653358,464684701656546,
%U A285371 5636371498958757,67862072916294706,814494099000392487,9780912755503955712,117894823818639390505,1430383074839724093993
%N A285371 Sum of the entries in the ninth blocks of all set partitions of [n].
%H A285371 Alois P. Heinz, <a href="/A285371/b285371.txt">Table of n, a(n) for n = 9..400</a>
%H A285371 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285371 a(n) = A285362(n,9).
%p A285371 a:= proc(h) option remember; local b; b:=
%p A285371       proc(n, m) option remember;
%p A285371         `if`(n=0, [1, 0], add((p-> `if`(j=9, p+ [0,
%p A285371         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285371       end: b(h, 0)[2]
%p A285371     end:
%p A285371 seq(a(n), n=9..30);
%t A285371 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 9, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285371 Table[a[n], {n, 9, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285371 Column k=9 of A285362.
%K A285371 nonn
%O A285371 9,1
%A A285371 _Alois P. Heinz_, Apr 17 2017