A246062 G.f.: sqrt( (1 + sqrt(1+8*x)) / (1 + sqrt(1-8*x)) ).

1, 2, 2, 28, 54, 860, 2004, 33720, 86054, 1492908, 4019452, 71101832, 198310460, 3555617432, 10168382696, 184127171952, 536496907782, 9788598556876, 28937139277804, 531135371147368, 1588378827366868, 29295861148032584, 88439788292856856, 1637711104368641552

Offset

0,2

Comments

Unsigned version of A193618.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

G.f.: sqrt( C(2*x)/C(-2*x) ) where C(x) = 1 + x*C(x)^2 is the Catalan function (A000108).

G.f.: exp( Sum_{n>=1} binomial(4*n-2,2*n-1)/2 * (2*x)^(2*n-1)/(2*n-1) ).

G.f. satisfies: A(x)*A(-x) = 1.

a(n) ~ sqrt(sqrt(2)-1)*(1+sqrt(2)-(-1)^n) * 2^(3*n-2) / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Aug 25 2014

Example

G.f.: A(x) = 1 + 2*x + 2*x^2 + 28*x^3 + 54*x^4 + 860*x^5 + 2004*x^6 +...

Mathematica

CoefficientList[Series[Sqrt[(1 + Sqrt[1 + 8*x])/(1 + Sqrt[1 - 8*x])], {x, 0, 20}], x] (* Vaclav Kotesovec, Aug 25 2014 *)

Prog

(PARI) {a(n)=polcoeff( sqrt((1+sqrt(1+8*x +O(x^(n+2))))/(1+sqrt(1-8*x +O(x^(n+2))))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A193618, A000108.

Sequence in context: A125067 A369755 A193618 * A178955 A012000 A116091

Adjacent sequences: A246059 A246060 A246061 * A246063 A246064 A246065

Keyword

nonn

Author

Paul D. Hanna, Aug 24 2014

Status

approved