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

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

Author

Seiichi Manyama, Jun 06 2018

Keywords

• nonn

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

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.