A278596 a(n) = Sum_{k=0..n} binomial(k+n+3,k)*binomial(2*n+1,n-k).

1, 8, 61, 462, 3504, 26664, 203632, 1560416, 11994112, 92445184, 714258944, 5530504192, 42905149440, 333427783680, 2595170856960, 20227227279360, 157854186209280, 1233319675822080, 9646098160680960, 75517231288811520

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000 (terms 0..282 from Carauleanu Marc)

Formula

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

a(n) ~ 9*2^(3*n-1)/sqrt(Pi*n). - Ilya Gutkovskiy, Nov 23 2016

Mathematica

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 *)

Prog

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

Crossrefs

Sequence in context: A283852 A283410 A081907 * A190976 A254602 A363571

Adjacent sequences: A278593 A278594 A278595 * A278597 A278598 A278599

Keyword

nonn

Author

Vladimir Kruchinin, Nov 23 2016

Status

approved