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Sum of the entries in the seventh blocks of all set partitions of [n].
2

%I #12 May 27 2018 10:31:48

%S 7,232,4518,67898,875365,10228471,111964040,1173487986,11959590504,

%T 119889568676,1192711559418,11859084564254,118526150123309,

%U 1196311505171568,12239696866561282,127315711586330538,1349476206629576995,14599608027440148129,161399084259928978190

%N Sum of the entries in the seventh blocks of all set partitions of [n].

%H Alois P. Heinz, <a href="/A285369/b285369.txt">Table of n, a(n) for n = 7..400</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>

%F a(n) = A285362(n,7).

%p a:= proc(h) option remember; local b; b:=

%p proc(n, m) option remember;

%p `if`(n=0, [1, 0], add((p-> `if`(j=7, p+ [0,

%p (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))

%p end: b(h, 0)[2]

%p end:

%p seq(a(n), n=7..30);

%t a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[Function[p, If[j == 7, p + {0, (h - n + 1)*p[[1]]}, p]][b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];

%t Table[a[n], {n, 7, 30}] (* _Jean-François Alcover_, May 27 2018, from Maple *)

%Y Column k=7 of A285362.

%K nonn

%O 7,1

%A _Alois P. Heinz_, Apr 17 2017