cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Seiichi Manyama, Jun 06 2018

Keywords

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

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.

Programs

  • 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

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.
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