cp's OEIS Frontend

A285424 Sum of the entries in the last blocks of all set partitions of [n].

%I A285424 #14 May 22 2018 03:01:21
%S A285424 1,5,19,75,323,1512,7630,41245,237573,1451359,9365361,63604596,
%T A285424 453206838,3378581609,26285755211,212953670251,1792896572319,
%U A285424 15658150745252,141619251656826,1324477898999161,12791059496663293,127395689514237279,1307010496324272157
%N A285424 Sum of the entries in the last blocks of all set partitions of [n].
%H A285424 Alois P. Heinz, <a href="/A285424/b285424.txt">Table of n, a(n) for n = 1..100</a>
%H A285424 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%e A285424 a(3) = 19 because the sum of the entries in the last blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 6+3+2+5+3 = 19.
%p A285424 a:= proc(h) option remember; local b; b:=
%p A285424       proc(n, m, s) option remember; `if`(n=0, s,
%p A285424         add(b(n-1, max(m, j), `if`(j<m, s, (h-n+1)+
%p A285424         `if`(j=m, s, 0))), j=1..m+1))
%p A285424       end: b(h, 0$2)
%p A285424     end:
%p A285424 seq(a(n), n=1..25);
%t A285424 a[h_] := a[h] = Module[{b}, b[n_, m_, s_] := b[n, m, s] = If[n == 0, s,   Sum[b[n-1, Max[m, j], If[j < m, s, h - n + 1 + If[j == m, s, 0]]], {j, 1, m + 1}]]; b[h, 0, 0]];
%t A285424 Array[a, 25] (* _Jean-François Alcover_, May 22 2018, translated from Maple *)
%Y A285424 Cf. A285362, A285363, A285382.
%Y A285424 Column k=1 of A286232.
%K A285424 nonn
%O A285424 1,2
%A A285424 _Alois P. Heinz_, Apr 18 2017