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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A305608 Expansion of 1/2 * (((1 + 4*x)/(1 - 4*x))^(1/4) - 1).

Original entry on oeis.org

0, 1, 1, 6, 11, 62, 138, 748, 1843, 9718, 25534, 131860, 362430, 1840940, 5233460, 26225496, 76546627, 379247782, 1130801782, 5548263172, 16838371978, 81921368964, 252369171404, 1218709491944, 3802973638254, 18243641612476, 57570352319788
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), this sequence (k=4), A305609 (k=8).
Cf. A303537.

Programs

  • Maple
    seq(coeff(series((1/2)*(((1+4*x)/(1-4*x))^(1/4)-1), x,35),x,n),n=0..30); # Muniru A Asiru, Jun 06 2018

Formula

n*a(n) = 2*a(n-1) + 16*(n-2)*a(n-2) for n > 1.
a(n) = A303537(n)/2 for n > 0.
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