A278596 - OEIS

%I #17 Apr 10 2017 23:00:45

%S 1,8,61,462,3504,26664,203632,1560416,11994112,92445184,714258944,

%T 5530504192,42905149440,333427783680,2595170856960,20227227279360,

%U 157854186209280,1233319675822080,9646098160680960,75517231288811520

%N a(n) = Sum_{k=0..n} binomial(k+n+3,k)*binomial(2*n+1,n-k).

%H G. C. Greubel, <a href="/A278596/b278596.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..282 from Carauleanu Marc)

%F G.f.: (sqrt(1-8*x)+3)^2/(2*(sqrt(1-8*x)+1)^3*sqrt(1-8*x)).

%F a(n) ~ 9*2^(3*n-1)/sqrt(Pi*n). - _Ilya Gutkovskiy_, Nov 23 2016

%t CoefficientList[Series[(Sqrt[1 - 8*x] + 3)^2/(2*(Sqrt[1 - 8*x] + 1)^3* Sqrt[1 - 8*x]), {x, 0, 50}], x] (* _G. C. Greubel_, Apr 09 2017 *)

%o (Maxima)

%o taylor((sqrt(1-8*x)+3)^2/(2*(sqrt(1-8*x)+1)^3*sqrt(1-8*x)),x,0,10);

%o (PARI) x='x+O('x^50); Vec((sqrt(1-8*x)+3)^2/(2*(sqrt(1-8*x) +1)^3*sqrt(1 -8*x))) \\ _G. C. Greubel_, Apr 09 2017

%K nonn

%O 0,2

%A _Vladimir Kruchinin_, Nov 23 2016