A098465 Expansion of (sqrt(1+3*x)-sqrt(1-5*x))/(4*x*sqrt(1-x)).

1, 1, 3, 7, 27, 91, 373, 1457, 6163, 25795, 111897, 486421, 2153429, 9584901, 43121211, 195082479, 888861555, 4069956979, 18732710281, 86579713685, 401776434017, 1870946532705, 8740907398527, 40956105551603

Offset

0,3

Comments

Binomial transform of A048990 (with interpolated zeros).

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..300

Formula

a(n) = sum{k=0..n} binomial(n,k) * C(k) * (1+(-1)^k)/2.

Recurrence: n*(n+1)*a(n) = 2*n*(2*n-1)*a(n-1) + 2*(5*n^2-10*n+3)*a(n-2) - 14*(n-2)*(2*n-3)*a(n-3) + 15*(n-3)*(n-2)*a(n-4). - Vaclav Kotesovec, Oct 24 2012

a(n) ~ 5^(n+3/2)/(16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 24 2012

Mathematica

CoefficientList[Series[(Sqrt[1+3*x]-Sqrt[1-5*x])/(4*x*Sqrt[1-x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)

Prog

(PARI) x='x+O('x^66); Vec((sqrt(1+3*x)-sqrt(1-5*x))/(4*x*sqrt(1-x))) \\ Joerg Arndt, May 11 2013

Crossrefs

Cf. A000108.

Sequence in context: A216078 A148748 A148749 * A148750 A081562 A216174

Adjacent sequences: A098462 A098463 A098464 * A098466 A098467 A098468

Keyword

easy,nonn

Author

Paul Barry, Sep 09 2004

Status

approved