OFFSET
0,2
LINKS
Robert Israel, Table of n, a(n) for n = 0..1694
FORMULA
a(n) = (-2)^n * Product_{i=0..n-1} (13-2*i) / n! for n>0. - R. J. Mathar, Feb 19 2008
D-finite with recurrence: n*a(n) - 2*(2*n-13)*a(n-1) = 0 for n>0. - Bruno Berselli, Jul 02 2018
a(n) ~ -135135 * 2^(2*n - 7) / (sqrt(Pi) * n^(15/2)). - Vaclav Kotesovec, Jul 02 2018
From Amiram Eldar, Mar 25 2022: (Start)
a(n) = (-4)^n*binomial(13/2, n).
Sum_{n>=0} 1/a(n) = 960/1001 - 10*Pi/(3^8*sqrt(3)).
Sum_{n>=0} (-1)^n/a(n) = 244659776/234609375 - 12*log(phi)/(5^7*sqrt(5)), where phi is the golden ratio (A001622). (End)
MAPLE
f := k -> -135135*(2*k)!/((2*k-1)*(2*k-3)*(2*k-5)*(2*k-7)*(2*k-9)*(2*k-11)*(-13+2*k)*(k!)^2):
map(f, [$0..30]); # Robert Israel, Jul 02 2018
MATHEMATICA
CoefficientList[Series[(1-4*x)^(13/2), {x, 0, 50}], x] (* Amiram Eldar, Mar 25 2022 *)
PROG
(PARI) my(x = 'x + O('x^40)); Vec((1-4*x)^(13/2)) \\ Michel Marcus, Jul 02 2018
CROSSREFS
KEYWORD
sign
AUTHOR
STATUS
approved