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URL: https://oeis.org/A305609

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A305609
Expansion of 1/2 * (((1 + 8*x)/(1 - 8*x))^(1/8) - 1).
2
0, 1, 1, 22, 43, 862, 2122, 40012, 111859, 2016566, 6130494, 106709364, 344744574, 5831760108, 19744810932, 326100935448, 1146472029123, 18549990711078, 67282629958006, 1069313429135204, 3982410828494666, 62297616737399876, 237367322452180556
OFFSET
0,4
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
FORMULA
n*a(n) = 2*a(n-1) + 64*(n-2)*a(n-2) for n > 1.
a(n) = A303538(n)/2 for n > 0.
MAPLE
seq(coeff(series((1/2)*(((1+8*x)/(1-8*x))^(1/8)-1), x, 30), x, n), n=0..25); # Muniru A Asiru, Jun 06 2018
CROSSREFS
1/2 * (((1 + k*x)/(1 - k*x))^(1/k) - 1): A001405(n-1) (k=2), A305608 (k=4), this sequence (k=8).
Cf. A303538.
Sequence in context: A086679 A019508 A166058 * A123799 A138842 A040462
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 06 2018
STATUS
approved