A098440 Expansion of 1/sqrt(1-2x-59x^2).

1, 1, 31, 91, 1531, 7051, 88201, 520381, 5529091, 37734931, 365291101, 2721338401, 24972058981, 196231466341, 1746558487831, 14182492489651, 124085095556851, 1028416533153331, 8913996083549341, 74841905963166481, 645571197111115201

Offset: 0

Author

Paul Barry, Sep 07 2004

Keywords

• easy
• nonn

Comments

9th binomial transform of 2^n*LegendreP(n,-4) Binomial transform of 1/sqrt(1-60x^2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.

Programs

Mathematica

CoefficientList[Series[1/Sqrt[1-2x-59x^2],{x,0,30}],x] (* Harvey P. Dale, Apr 25 2012 *)

PARI

x='x+O('x^66); Vec(1/sqrt(1-2*x-59*x^2)) \\ Joerg Arndt, May 11 2013

Formula

a(n) = sum{k=0..floor(n/2), binomial(n-k, k)*binomial(n, k)*15^k}.

D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) + 59*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 15 2012

a(n) ~ sqrt(450+15*sqrt(15))*(1+2*sqrt(15))^n/(30*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012