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A304940
Expansion of ((1 + 4*x)/(1 - 4*x))^(1/2).
2
1, 4, 8, 32, 96, 384, 1280, 5120, 17920, 71680, 258048, 1032192, 3784704, 15138816, 56229888, 224919552, 843448320, 3373793280, 12745441280, 50981765120, 193730707456, 774922829824, 2958796259328, 11835185037312, 45368209309696, 181472837238784
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
FORMULA
n*a(n) = 4*a(n-1) + 4^2*(n-2)*a(n-2) for n > 1.
a(n) = 2^n * A063886(n).
PROG
(PARI) N=66; x='x+O('x^N); Vec(((1+4*x)/(1-4*x))^(1/2))
CROSSREFS
((1 + 4*x)/(1 - 4*x))^(m/4): A303537 (m=1), this sequence (m=2), A304941 (m=3), A081654 (m=4).
Cf. A063886.
Sequence in context: A086344 A209084 A254216 * A068205 A241684 A254878
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 22 2018
STATUS
approved