OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..1430
FORMULA
G.f.: ((1-x)^3*(1-sqrt((5*x-1)/(x-1))))/(2*x).
a(n) ~ 8*5^(n-3/2) / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Nov 07 2016
(5*n-10)*a(n)-(7+6*n)*a(n+1)+(n+3)*a(n+2)=0 for n >= 2. - Robert Israel, Nov 21 2016
a(n) = A055452(n+1) for n > 2. - Georg Fischer, Oct 23 2018
MAPLE
f:= gfun:-rectoproc({(5*n-10)*a(n)+(-7-6*n)*a(n+1)+(n+3)*a(n+2), a(0) = 1, a(1) = -1, a(2) = 2, a(3) = 5}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Nov 21 2016
MATHEMATICA
CoefficientList[Series[((1 - x)^3 (1 - Sqrt[(5 x - 1) / (x - 1)])) / (2 x), {x, 0, 25}], x] (* Vincenzo Librandi, Nov 07 2016 *)
PROG
(Maxima)
a(n):=sum((binomial(2*k, k)*binomial(n-3, n-k))/(k+1), k, 0, n);
(PARI) x='x+O('x^50); Vec(((1-x)^3*(1-sqrt((5*x-1)/(x-1))))/(2*x)) \\ G. C. Greubel, Apr 09 2017
CROSSREFS
KEYWORD
sign
AUTHOR
Vladimir Kruchinin, Nov 06 2016
STATUS
approved