OFFSET
0,2
COMMENTS
Let 1/2 * (((1 + k*x)/(1 - k*x))^(m/k) - 1) = a(0) + a(1)*x + a(2)*x^2 + ...
Then n*a(n) = 2*m*a(n-1) + k^2*(n-2)*a(n-2) for n > 1.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..3000
FORMULA
n*a(n) = 6*a(n-1) + 4*(n-2)*a(n-2) for n > 1.
a(n) = A305031(n)/2 for n > 0.
MAPLE
seq(coeff(series((1/2)*(((1+2*x)/(1-2*x))^(3/2)-1), x, n+1), x, n), n=0..35); # Muniru A Asiru, Jun 06 2018
MATHEMATICA
CoefficientList[Series[((((1+2x)/(1-2x))^(3/2))-1)/2, {x, 0, 40}], x] (* Harvey P. Dale, Nov 04 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 06 2018
STATUS
approved