OFFSET
0,3
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.
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
MATHEMATICA
CoefficientList[Series[1/Sqrt[1-2x-59x^2], {x, 0, 30}], x] (* Harvey P. Dale, Apr 25 2012 *)
PROG
(PARI) x='x+O('x^66); Vec(1/sqrt(1-2*x-59*x^2)) \\ Joerg Arndt, May 11 2013
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Sep 07 2004
STATUS
approved