OFFSET
0,5
COMMENTS
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: A(x) = (1 + 2*x)/(1+x)/(1+x - x^2*Catalan(-x)^2), where Catalan(x)=(1-(1-4*x)^(1/2))/(2*x) (cf. A000108).
a(n) ~ (-1)^n * 2^(2*n+1) / (3*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Mar 06 2014
D-finite with recurrence: (n+1)*a(n) +(7*n-3)*a(n-1) +2*(7*n-12)*a(n-2) +4*(2*n-5)*a(n-3)=0. - R. J. Mathar, Jan 23 2020
MAPLE
gf := (2*(2*x+1))/((x+1)*(sqrt(4*x+1)+1)): ser := series(gf, x, 30):
seq(coeff(ser, x, n), n=0..28); # Peter Luschny, Apr 25 2016
MATHEMATICA
CoefficientList[Series[(1+2*x)/(1+x)/(1+x - (1-(1+4*x)^(1/2))^2/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 06 2014 *)
PROG
(PARI) {a(n)=local(X=x+x*O(x^n)); polcoeff( (1+2*X)/(1+X)/(1+X-(1-(1+4*X)^(1/2))^2/4), n, x)}
(Python)
from itertools import accumulate
def A104496_list(size):
if size < 1: return []
L, accu = [1], [1]
for n in range(size-1):
accu = list(accumulate(accu + [-accu[0]]))
L.append(-(-1)**n*accu[-1])
return L
print(A104496_list(29)) # Peter Luschny, Apr 25 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul D. Hanna, Mar 11 2005
EXTENSIONS
New name using the g.f. of the author by Peter Luschny, Apr 25 2016
STATUS
approved