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A285363 Sum of the entries in the first blocks of all set partitions of [n].

%I A285363 #15 May 20 2018 11:36:14
%S A285363 1,4,15,60,262,1243,6358,34835,203307,1257913,8216945,56463487,
%T A285363 406868167,3065920770,24099977863,197179545722,1675846476148,
%U A285363 14769104672839,134745258569108,1270767279092285,12371426210292311,124173909409948575,1283498833928098171
%N A285363 Sum of the entries in the first blocks of all set partitions of [n].
%H A285363 Alois P. Heinz, <a href="/A285363/b285363.txt">Table of n, a(n) for n = 1..575</a>
%H A285363 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285363 a(n) = A285362(n,1).
%e A285363 a(3) = 15 because the sum of the entries in the first blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 6+3+4+1+1 = 15.
%p A285363 a:= proc(h) option remember; local b; b:=
%p A285363       proc(n, m) option remember;
%p A285363         `if`(n=0, [1, 0], add((p-> `if`(j=1, p+ [0,
%p A285363         (h-n+1)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285363       end: b(h, 0)[2]
%p A285363     end:
%p A285363 seq(a(n), n=1..30);
%t A285363 a[h_] := a[h] = Module[{b}, b[n_, m_] := b[n, m] = If[n == 0, {1, 0}, Sum[If[j == 1, # + {0, (h - n + 1)*#[[1]]}, #]&[b[n - 1, Max[m, j]]], {j, 1, m + 1}]]; b[h, 0][[2]]];
%t A285363 Table[a[n], {n, 1, 30}] (* _Jean-François Alcover_, May 20 2018, translated from Maple *)
%Y A285363 Column k=1 of A285362.
%Y A285363 Cf. A284816, A285424.
%K A285363 nonn
%O A285363 1,2
%A A285363 _Alois P. Heinz_, Apr 17 2017