A174516 Partial sums of A002896.
1, 7, 97, 1957, 46687, 1219243, 33715399, 970085119, 28740443449, 870830918389, 26860099935529, 840549807424369, 26620996978712269, 851664885506669269, 27482469263443730269, 893460843597349019629, 29235859228655427097639
Offset: 0
Keywords
Examples
a(4) = 1 + 6 + 90 + 1860 + 44730 = 46687.
Programs
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Mathematica
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 *)
Formula
a(n) = Sum_{i=0..n} A002896(i).
G.f.: g/(1-x) where g is the o.g.f. of A002896. - Mark van Hoeij, Nov 12 2011
a(n) ~ 2^(2*n) * 3^(2*n + 7/2) / (35 * Pi^(3/2) * n^(3/2)). - Vaclav Kotesovec, Feb 17 2024