A128419 Expansion of 8/(sqrt(1-8*x)*(sqrt(1-8*x)+4*x+7)).
1, 4, 25, 168, 1181, 8524, 62609, 465616, 3495013, 26423604, 200920985, 1534936440, 11771854381, 90578698396, 698921030945, 5406132020128, 41905249405301, 325434733291396, 2531523208218665, 19721766268370248, 153847524455503421, 1201601094053039596, 9395224234956935345
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..300
Programs
-
Mathematica
CoefficientList[Series[8/(Sqrt[1-8x](Sqrt[1-8x]+4x+7)),{x,0,30}],x] (* Harvey P. Dale, Apr 24 2012 *) Table[Sum[2^(n-2*k)*Binomial[2*n-2*k,n-2*k], {k,0,Floor[n/2]}],{n,0,50}] (* G. C. Greubel, Feb 09 2017 *) -
PARI
x='x+O('x^50); Vec(8/(sqrt(1-8*x)*(sqrt(1-8*x)+4*x+7))) \\ G. C. Greubel, Feb 09 2017
Formula
a(n) = Sum_{k=0..floor(n/2)} 2^(n-2k)*C(2n-2k,n-2k).
D-finite with recurrence: 3*n*(15*n-22)*a(n) = 4*(75*n^2-155*n+63)*a(n-1) + (465*n^2-922*n+336)*a(n-2) + 4*(2*n-3)*(15*n-7)*a(n-3) . - Vaclav Kotesovec, Oct 20 2012
a(n) ~ 2^(3*n+4)/(15*sqrt(Pi*n)) . - Vaclav Kotesovec, Oct 20 2012
Comments