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*(1-x)*sqrt(1-4*x)). - Ilya Gutkovskiy, Jun 15 2016
From Mélika Tebni, Sep 02 2024: (Start)
E.g.f.: exp(2*x)*(5*BesselI(0, 2*x)/2 + BesselI(1, 2*x)) + exp(x)/2*(3*Integral_{x=-oo..oo} BesselI(0,2*x)*exp(x) dx - 1). (End)
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 *)
PROG
(Magma) [(&+[(3*k+2)*Catalan(k): k in [0..n]]): n in [0..40]]; // G. C. Greubel, Jun 30 2024
(SageMath) [sum((3*k+2)*catalan_number(k) for k in range(n+1)) for n in range(41)] # G. C. Greubel, Jun 30 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 13 2016
STATUS
approved