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A305608
Expansion of 1/2 * (((1 + 4*x)/(1 - 4*x))^(1/4) - 1).
2
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
0,4
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) + 16*(n-2)*a(n-2) for n > 1.
a(n) = A303537(n)/2 for n > 0.
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
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.
Sequence in context: A073219 A365496 A110445 * A128387 A061519 A193664
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jun 06 2018
STATUS
approved