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A304915
Expansion of ((1 + 16*x)/(1 - 16*x))^(1/16).
1
1, 2, 2, 172, 342, 26556, 67220, 4875160, 14125030, 973837420, 3087573628, 204536051176, 692771715836, 44412235657176, 158358513025896, 9874709152875568, 36706645561910150, 2234840966950941260, 8601116786415880940, 512801585354912006600, 2032977466125710169236
OFFSET
0,2
COMMENTS
Let ((1 + k*x)/(1 - k*x))^(1/k) = a(0) + a(1)*x + a(2)*x^2 + ...
Then n*a(n) = 2*a(n-1) + k^2*(n-2)*a(n-2) for n > 1.
LINKS
FORMULA
n*a(n) = 2*a(n-1) + 16^2*(n-2)*a(n-2) for n > 1.
a(n) ~ 2^(4*n + 1/16) / (Gamma(1/16) * n^(15/16)) * (1 - (-1)^n * sqrt(2 - sqrt(2 + sqrt(2))) * 2^(7/8) * Gamma(1/16)^2 / (64*Pi*n^(1/8))). - Vaclav Kotesovec, May 21 2018
MATHEMATICA
CoefficientList[Series[((1+16x)/(1-16x))^(1/16), {x, 0, 30}], x] (* Harvey P. Dale, Jul 21 2021 *)
PROG
(PARI) N=66; x='x+O('x^N); Vec(((1+16*x)/(1-16*x))^(1/16))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 21 2018
STATUS
approved