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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 (list; graph; refs; listen; history; text; internal format)
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

Seiichi Manyama, Table of n, a(n) for n = 0..500

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

PROG

(PARI) N=66; x='x+O('x^N); Vec(((1+16*x)/(1-16*x))^(1/16))

CROSSREFS

Cf. A063886, A303537, A303538.

Sequence in context: A194027 A003110 A100956 * A216481 A078241 A216812

Adjacent sequences:  A304912 A304913 A304914 * A304916 A304917 A304918

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 21 2018

STATUS

approved

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Last modified December 10 18:10 EST 2019. Contains 329901 sequences. (Running on oeis4.)