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A270501 Sum of the sizes of the ninth blocks in all set partitions of {1,2,...,n}.

%I A270501 #10 May 27 2018 02:29:29
%S A270501 1,47,1267,25820,443249,6782968,95737722,1274661371,16262852622,
%T A270501 201150251360,2433394489974,28994047438464,342194356303003,
%U A270501 4019284858043011,47169786677194389,555004306379162344,6566292430043177959,78313245092235242824,943595956075419339524
%N A270501 Sum of the sizes of the ninth blocks in all set partitions of {1,2,...,n}.
%H A270501 Alois P. Heinz, <a href="/A270501/b270501.txt">Table of n, a(n) for n = 9..575</a>
%H A270501 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A270501 b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p A270501       add((p->`if`(j<10, [p[1], p[2]+p[1]*x^j], p))(
%p A270501        b(n-1, max(m, j))), j=1..m+1))
%p A270501     end:
%p A270501 a:= n-> coeff(b(n, 0)[2], x, 9):
%p A270501 seq(a(n), n=9..30);
%t A270501 b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 10, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
%t A270501 a[n_] := Coefficient[b[n, 0][[2]], x, 9];
%t A270501 Table[a[n], {n, 9, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A270501 Column p=9 of A270236.
%K A270501 nonn
%O A270501 9,2
%A A270501 _Alois P. Heinz_, Mar 18 2016