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%I A174516 #19 Feb 17 2024 03:08:14
%S A174516 1,7,97,1957,46687,1219243,33715399,970085119,28740443449,
%T A174516 870830918389,26860099935529,840549807424369,26620996978712269,
%U A174516 851664885506669269,27482469263443730269,893460843597349019629,29235859228655427097639
%N A174516 Partial sums of A002896.
%F A174516 a(n) = Sum_{i=0..n} A002896(i).
%F A174516 G.f.: g/(1-x) where g is the o.g.f. of A002896. - _Mark van Hoeij_, Nov 12 2011
%F A174516 a(n) ~ 2^(2*n) * 3^(2*n + 7/2) / (35 * Pi^(3/2) * n^(3/2)). - _Vaclav Kotesovec_, Feb 17 2024
%e A174516 a(4) = 1 + 6 + 90 + 1860 + 44730 = 46687.
%t A174516 b[n_] := b[n] = (* A002896 *) Binomial[2*n, n]*HypergeometricPFQ[{1/2, -n, -n}, {1, 1}, 4]; a[n_] := Sum[b[k], {k, 0, n}]; Table[a[n], {n, 0, 16}] (* _Jean-François Alcover_, Dec 20 2011 *)
%Y A174516 Cf. A002896, A049020, A049037, A084261, A138540, A140476.
%K A174516 nonn
%O A174516 0,2
%A A174516 _Jonathan Vos Post_, Mar 20 2010

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