OFFSET
0,2
COMMENTS
FORMULA
a(n) = 2^(2*n)*(2*n)!*[x^(2*n)] cos(x/sqrt(2))^(-2). - Peter Luschny, Sep 03 2022
MAPLE
eulerCF := proc(f, len) local g, k; g := 1;
for k from len-2 by -1 to 0 do g := 1 - f(k)/(f(k)-1/g) od;
PolynomialTools:-CoefficientList(convert(series(g, x, len), polynom), x) end:
# Alternative:
ser := series(cos(x/sqrt(2))^(-2), x, 32):
seq(2^(2*n)*(2*n)!*coeff(ser, x, 2*n), n = 0..15); # Peter Luschny, Sep 03 2022
MATHEMATICA
fracGen[f_, len_] := Module[{g, k}, g[len] = 1; For[k = len-1, k >= 0, k--, g[k] = 1-f[k]/(f[k]-1/g[k+1])]; CoefficientList[g[0] + O[x]^(len+1), x] ]; A261042list[len_] := fracGen[x*2*(#+1)*(#+2)&, len-1]; A261042list[16] (* Jean-François Alcover, Aug 08 2015, after Peter Luschny *)
PROG
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Aug 08 2015
STATUS
approved