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%I #18 Dec 11 2022 13:21:03
%S 2,7,23,78,274,988,3628,13495,50675,191673,729145,2786655,10691111,
%T 41150011,158825371,614483086,2382366586,9253540456,36001307656,
%U 140269835866,547245301906,2137552658206,8358366985726,32715599554876,128168506456852,502538379368656,1971926625140816
%N a(n) = Sum_{k=0..n} (3*k+2)*Catalan(k).
%H Vincenzo Librandi, <a href="/A274104/b274104.txt">Table of n, a(n) for n = 0..200</a>
%H Moa Apagodu and Doron Zeilberger, <a href="http://arxiv.org/abs/1606.03351">Using the "Freshman's Dream" to Prove Combinatorial Congruences</a>, arXiv:1606.03351 [math.CO], 2016. Also Amer. Math. Monthly. 124 (2017), 597-608.
%F 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
%F G.f.: (1 + 2*x - sqrt(1-4*x))/(2*x*sqrt(1-4*x)*(1 - x)). - _Ilya Gutkovskiy_, Jun 15 2016
%t 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 *)
%Y Partial sums of A051960.
%Y Cf. A000108.
%K nonn
%O 0,1
%A _N. J. A. Sloane_, Jun 13 2016
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