OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: (1/2)*(sqrt(4*x+1)*(1+x)-3*x-1)/(sqrt(4*x+1)*(x^2+3*x+1)-4*x^2-5*x-1). - Vladimir Kruchinin, Mar 28 2016
a(n) ~ (-1)^(n+1) *2^(2*n+1) / (5*sqrt(Pi*n)). - Vaclav Kotesovec, Mar 28 2016
Conjecture: +2*n*a(n) +8*n*a(n-1) +(-n+20)*a(n-2) +5*(-n+4)*a(n-3) +2*(-2*n+5)*a(n-4)=0. - R. J. Mathar, Jun 14 2016
MATHEMATICA
f[n_] := Sum[ Binomial[n + k, k] Sin[Pi (n + k)/2], {k, 0, n}]; Array[f, 25, 0]
PROG
(Maxima)
makelist(coeff(taylor(1/2*(sqrt(4*x+1)*(1+x)-3*x-1)/(sqrt(4*x+1)*(x^2+3*x+1)-4*x^2-5*x-1), x, 0, 20), x, n), n, 0, 20) /* Vladimir Kruchinin, Mar 28 2016 */
(PARI) x='x+O('x^50); concat([0], Vec((1/2)*(sqrt(4*x+1)*(1+x)-3*x-1)/(sqrt(4*x+1)*(x^2+3*x+1)-4*x^2-5*x-1))) \\ G. C. Greubel, Mar 24 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Robert G. Wilson v, Apr 02 2012
STATUS
approved