OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
G.f.: (1+x-sqrt(1-2*x-15*x^2))/(2*x) - C. Ronaldo (aga_new_ac(AT)hotmail.com), Dec 19 2004
a(n) = (-3)^n*(hypergeom([1/2, n+1],[1],8/5)-5*hypergeom([1/2, n],[1],8/5))*(-15)^(1/2)/(10*(n+1)) for n>0. - Mark van Hoeij, Jul 02 2010
Recurrence: (n+1)*a(n) = (2*n-1)*a(n-1) + 15*(n-2)*a(n-2). - Vaclav Kotesovec, Oct 07 2012
a(n) ~ 5^(n+1/2)/(sqrt(2*Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 07 2012
a(n) = (-2)^(n+1)*C(2*n,n-1)*hypergeom([-n-1,-n+1],[-n+1/2],5/8)/n for n>=1. - Peter Luschny, May 08 2016
a(n) = 2^(n+1)*GegenbauerC(n-1,-n,-1/4)/n for n>=1. - Peter Luschny, May 08 2016
G.f.: 1 + 4*x/G(x) with G(x) = (1 - x - 4*x^2/G(x)) (continued fraction). - Nikolaos Pantelidis, Jan 09 2023
MAPLE
a := n -> `if`(n=0, 1, simplify(2^(n+1)*GegenbauerC(n-1, -n, -1/4)/n)):
seq(a(n), n=0..26); # Peter Luschny, May 08 2016
MATHEMATICA
Table[SeriesCoefficient[(1+x-Sqrt[1-2*x-15*x^2])/(2*x), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 07 2012 *)
nxt[{n_, a_, b_}]:={n+1, b, (b(2n+1)+15a(n-1))/(n+2)}; NestList[nxt, {1, 1, 4}, 30][[All, 2]] (* Harvey P. Dale, Jul 07 2019 *)
PROG
(PARI) x='x+O('x^66); Vec((1+x-sqrt(1-2*x-15*x^2))/(2*x)) \\ Joerg Arndt, May 04 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved