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A285370 Sum of the entries in the eighth blocks of all set partitions of [n].

%I A285370 #10 Nov 22 2024 06:18:34
%S A285370 8,333,7995,145814,2250020,31075944,397434249,4813480830,56089581910,
%T A285370 636257739216,7090058863984,78176548855068,858005254659222,
%U A285370 9419825826737075,103885234357070729,1154951013922367450,12982852258320087936,147928345019800310188
%N A285370 Sum of the entries in the eighth blocks of all set partitions of [n].
%H A285370 Alois P. Heinz, <a href="/A285370/b285370.txt">Table of n, a(n) for n = 8..400</a>
%H A285370 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285370 a(n) = A285362(n,8).
%p A285370 a:= proc(h) option remember; local b; b:=
%p A285370       proc(n, m) option remember;
%p A285370         `if`(n=0, [1, 0], add((p-> `if`(j=8, p+ [0,
%p A285370         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285370       end: b(h, 0)[2]
%p A285370     end:
%p A285370 seq(a(n), n=8..30);
%t A285370 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 8, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285370 Table[a[n], {n, 8, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285370 Column k=8 of A285362.
%K A285370 nonn
%O A285370 8,1
%A A285370 _Alois P. Heinz_, Apr 17 2017