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A285372 Sum of the entries in the tenth blocks of all set partitions of [n].

%I A285372 #7 May 27 2018 08:09:14
%S A285372 10,616,21318,547857,11676343,218761153,3732864275,59392240551,
%T A285372 895833879036,12967143328027,181820930739504,2487908867278337,
%U A285372 33420903985242540,442951837401015291,5816787707500820380,75959640100454216760,989568067595589010921
%N A285372 Sum of the entries in the tenth blocks of all set partitions of [n].
%H A285372 Alois P. Heinz, <a href="/A285372/b285372.txt">Table of n, a(n) for n = 10..400</a>
%H A285372 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285372 a(n) = A285362(n,10).
%p A285372 a:= proc(h) option remember; local b; b:=
%p A285372       proc(n, m) option remember;
%p A285372         `if`(n=0, [1, 0], add((p-> `if`(j=10, p+ [0,
%p A285372         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285372       end: b(h, 0)[2]
%p A285372     end:
%p A285372 seq(a(n), n=10..30);
%t A285372 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 10, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285372 Table[a[n], {n, 10, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)
%Y A285372 Column k=10 of A285362.
%K A285372 nonn
%O A285372 10,1
%A A285372 _Alois P. Heinz_, Apr 17 2017