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A270500 Sum of the sizes of the eighth blocks in all set partitions of {1,2,...,n}.

%I A270500 #10 May 27 2018 02:29:21
%S A270500 1,38,842,14303,207186,2704647,32890525,380797185,4261887992,
%T A270500 46630717274,503083676180,5388429971042,57614949228381,
%U A270500 617784630625192,6668316674283818,72685580775510461,802184346241503206,8983104653288906449,102246823195952449865
%N A270500 Sum of the sizes of the eighth blocks in all set partitions of {1,2,...,n}.
%H A270500 Alois P. Heinz, <a href="/A270500/b270500.txt">Table of n, a(n) for n = 8..575</a>
%H A270500 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%p A270500 b:= proc(n, m) option remember; `if`(n=0, [1, 0],
%p A270500       add((p->`if`(j<9, [p[1], p[2]+p[1]*x^j], p))(
%p A270500        b(n-1, max(m, j))), j=1..m+1))
%p A270500     end:
%p A270500 a:= n-> coeff(b(n, 0)[2], x, 8):
%p A270500 seq(a(n), n=8..30);
%t A270500 b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j < 9, {p[[1]], p[[2]] + p[[1]]*x^j}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]];
%t A270500 a[n_] := Coefficient[b[n, 0][[2]], x, 8];
%t A270500 Table[a[n], {n, 8, 30}] (* _Jean-François Alcover_, May 27 2018, translated from Maple *)
%Y A270500 Column p=8 of A270236.
%K A270500 nonn
%O A270500 8,2
%A A270500 _Alois P. Heinz_, Mar 18 2016