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A285410 Sum of the entries in the (n+1)-th blocks of all set partitions of [2n+1].

%I A285410 #12 May 24 2018 08:43:16
%S A285410 1,12,185,3757,96454,3018824,111964040,4813480830,235727269842,
%T A285410 12967143328027,792113203502422,53224214308284463,3902445739220008603,
%U A285410 310108348556403600064,26551900616231571763742,2437107937223749442138164,238735439946016510599661488
%N A285410 Sum of the entries in the (n+1)-th blocks of all set partitions of [2n+1].
%H A285410 Alois P. Heinz, <a href="/A285410/b285410.txt">Table of n, a(n) for n = 0..345</a>
%H A285410 Wikipedia, <a href="https://en.wikipedia.org/wiki/Partition_of_a_set">Partition of a set</a>
%F A285410 a(n) = A285362(2n+1,n+1).
%e A285410 a(1) = 12 because the sum of the entries in the second blocks of all set partitions of [3] (123, 12|3, 13|2, 1|23, 1|2|3) is 0+3+2+5+2 = 12.
%p A285410 a:= proc(h) option remember; local b; b:=
%p A285410       proc(n, m) option remember;
%p A285410         `if`(n=0, [1, 0], add((p-> `if`(j=h+1, p+ [0,
%p A285410         (2*h-n+2)*p[1]], p))(b(n-1, max(m, j))), j=1..m+1))
%p A285410       end: b(2*h+1, 0)[2]
%p A285410     end:
%p A285410 seq(a(n), n=0..20);
%t A285410 a[h_] := a[h] = Module[{b}, b[0, _] = {1, 0}; b[n_, m_] := b[n, m] = Sum[ If[j == h + 1, # + {0, (2*h - n + 2)*#[[1]]}, #]&[b[n - 1, Max[m, j]]], {j, 1, m + 1}]; b[2*h + 1, 0][[2]]];
%t A285410 Table[a[n], {n, 0, 20}] (* _Jean-François Alcover_, May 23 2018, translated from Maple *)
%Y A285410 Cf. A270529, A285362.
%K A285410 nonn
%O A285410 0,2
%A A285410 _Alois P. Heinz_, Apr 18 2017