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A303537 Expansion of ((1 + 4*x)/(1 - 4*x))^(1/4). 7
1, 2, 2, 12, 22, 124, 276, 1496, 3686, 19436, 51068, 263720, 724860, 3681880, 10466920, 52450992, 153093254, 758495564, 2261603564, 11096526344, 33676743956, 163842737928, 504738342808, 2437418983888, 7605947276508, 36487283224952, 115140704639576 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let ((1 + k*x)/(1 - k*x))^(1/k) = a(0) + a(1)*x + a(2)*x^2 + ...

Then n*a(n) = 2*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

a(n) ~ 2^(2*n + 1/4) / (Gamma(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 26 2018

n*a(n) = 2*a(n-1) + 4^2*(n-2)*a(n-2) for n > 1.

PROG

(PARI) N=66; x='x+O('x^N); Vec(((1+4*x)/(1-4*x))^(1/4))

CROSSREFS

Cf. A063886, A081654, A303538.

Sequence in context: A178845 A140431 A092900 * A164961 A122007 A137782

Adjacent sequences:  A303534 A303535 A303536 * A303538 A303539 A303540

KEYWORD

nonn

AUTHOR

Seiichi Manyama, Apr 25 2018

STATUS

approved

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Last modified August 18 16:13 EDT 2018. Contains 313833 sequences. (Running on oeis4.)