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A304941 Expansion of ((1 + 4*x)/(1 - 4*x))^(3/4). 4
1, 6, 18, 68, 246, 948, 3572, 13896, 53286, 208452, 807132, 3169080, 12346300, 48602760, 190150440, 750018448, 2943363078, 11627329764, 45736940364, 180897649368, 712881236052, 2822389182104, 11138924119512, 44137230865392, 174405194802524, 691557285091176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Let ((1 + k*x)/(1 - k*x))^(m/k) = 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

FORMULA

n*a(n) = 6*a(n-1) + 4^2*(n-2)*a(n-2) for n > 1.

a(n) ~ 2^(2*n + 3/4) / (Gamma(3/4) * n^(1/4)). - Vaclav Kotesovec, May 28 2018

PROG

(PARI) N=66; x='x+O('x^N); Vec(((1+4*x)/(1-4*x))^(3/4))

CROSSREFS

((1 + 4*x)/(1 - 4*x))^(m/4): A303537 (m=1), A304940 (m=2), this sequence (m=3), A081654 (m=4).

Sequence in context: A034751 A200151 A000623 * A129369 A095853 A027266

Adjacent sequences:  A304938 A304939 A304940 * A304942 A304943 A304944

KEYWORD

nonn

AUTHOR

Seiichi Manyama, May 22 2018

STATUS

approved

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Last modified August 8 02:45 EDT 2020. Contains 336290 sequences. (Running on oeis4.)