A247102 Expansion of g.f. (6*x+2)/(sqrt(-3*x^2-6*x+1)*(4*x^2+4*x)) - (2*x+1)/(2*x^2+2*x).

2, 10, 53, 298, 1727, 10207, 61154, 370090, 2256983, 13848085, 85387040, 528646015, 3284180720, 20462505850, 127816245053, 800143927210, 5018683475087, 31532297088781, 198419993271440, 1250291989478773, 7888160383113014

Offset

0,1

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = Sum_{i=0..n+1} binomial(2*n-i+1,n-i+1)*(Sum_{j=0..n+1} binomial(j,-j+i)*binomial(n+1,j)).

a(n) ~ sqrt(3) * (3+2*sqrt(3))^(n+1) / (2*sqrt(2*Pi*n)). - Vaclav Kotesovec, Nov 23 2014

Conjecture D-finite with recurrence: (n+1)*a(n) +(-2*n-5)*a(n-1) +3*(-8*n+7)*a(n-2) +15*(-2*n+3)*a(n-3) +9*(-n+2)*a(n-4)=0. - R. J. Mathar, Jan 25 2020

Mathematica

CoefficientList[Series[(6 x + 2) / (Sqrt[-3 x^2 - 6 x + 1] (4 x^2 + 4 x)) - (2 x + 1) / (2 x^2 + 2 x), {x, 0, 40}], x] (* Vincenzo Librandi, Nov 22 2014 *)

Prog

(Maxima)
a(n):=sum(binomial(2*n-i+1, n-i+1)*sum(binomial(j, -j+i)*binomial(n+1, j), j, 0, n+1), i, 0, n+1);

Crossrefs

Sequence in context: A037619 A221610 A378403 * A370390 A009320 A204186

Adjacent sequences: A247099 A247100 A247101 * A247103 A247104 A247105

Keyword

nonn

Author

Vladimir Kruchinin, Nov 22 2014

Status

approved