A305609 Expansion of 1/2 * (((1 + 8*x)/(1 - 8*x))^(1/8) - 1).

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

Seiichi Manyama, Table of n, a(n) for n = 0..1000

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

Adjacent sequences: A305606 A305607 A305608 * A305610 A305611 A305612

Keyword

nonn

Author

Seiichi Manyama, Jun 06 2018

Status

approved