OFFSET
0,3
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
FORMULA
MAPLE
a := proc(n) option remember; if n < 3 then return [1, -1, 5][n+1] fi;
(-36*(n - 2)*a(n-3) + 6*(4*n - 5)*a(n-2) - (n - 5)*a(n-1))/(n + 1) end:
seq(a(n), n=0..24);
# Alternative:
gf := 2/(sqrt(4*x - 12*x^2 + 1) + 1):
ser := series(gf, x, 30): seq(coeff(ser, x, n), n=0..24);
# Or:
series((x^2+x)/(3*x^2+1), x, 30): gfun:-seriestoseries(%, 'revogf'):
convert(%, polynom) / x: seq(coeff(%, x, n), n=0..24);
MATHEMATICA
A330800[n_]:= Coefficient[Series[2/(Sqrt[4*x-12*x^2+1] +1), {x, 0, 50}], x, n]; Table[A330800[n], {n, 0, 30}] (* G. C. Greubel, Sep 13 2023 *)
PROG
(SageMath)
R.<x> = PowerSeriesRing(QQ)
f = (x^2 + x)/(3*x^2 + 1)
f.reverse().shift(-1).list()
(Magma) I:=[1, -1, 5]; [n le 3 select I[n] else ((6-n)*Self(n-1) + 6*(4*n-9)*Self(n-2) -36*(n-3)*Self(n-3))/n: n in [1..30]]; // G. C. Greubel, Sep 13 2023
CROSSREFS
KEYWORD
sign
AUTHOR
Peter Luschny, Jan 01 2020
STATUS
approved