A274104 a(n) = Sum_{k=0..n} (3*k+2)*Catalan(k).

2, 7, 23, 78, 274, 988, 3628, 13495, 50675, 191673, 729145, 2786655, 10691111, 41150011, 158825371, 614483086, 2382366586, 9253540456, 36001307656, 140269835866, 547245301906, 2137552658206, 8358366985726, 32715599554876, 128168506456852, 502538379368656, 1971926625140816

Offset

0,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Moa Apagodu and Doron Zeilberger, Using the "Freshman's Dream" to Prove Combinatorial Congruences, arXiv:1606.03351 [math.CO], 2016. Also Amer. Math. Monthly. 124 (2017), 597-608.

Formula

D-finite with recurrence: (n+1)*a(n) +(-3*n-5)*a(n-1) +2*(-3*n+8)*a(n-2) +4*(2*n-3)*a(n-3)=0. - R. J. Mathar, Jun 15 2016

G.f.: (1 + 2*x - sqrt(1-4*x))/(2*x*sqrt(1-4*x)*(1 - x)). - Ilya Gutkovskiy, Jun 15 2016

Mathematica

CoefficientList[Series[(1 + 2 x - Sqrt[1 - 4 x]) / (2 x Sqrt[1 - 4 x] (1 - x)), {x, 0, 50}], x] (* Vincenzo Librandi, Aug 18 2016 *)

Crossrefs

Partial sums of A051960.

Cf. A000108.

Sequence in context: A292236 A292087 A091702 * A068593 A198944 A328035

Adjacent sequences: A274101 A274102 A274103 * A274105 A274106 A274107

Keyword

nonn

Author

N. J. A. Sloane, Jun 13 2016

Status

approved