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A305612
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Expansion of 1/2 * (((1 + 2*x)/(1 - 2*x))^(3/2) - 1).
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1
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0, 3, 9, 22, 51, 114, 250, 540, 1155, 2450, 5166, 10836, 22638, 47124, 97812, 202488, 418275, 862290, 1774630, 3646500, 7482618, 15334748, 31391724, 64194312, 131151566, 267711444, 546031500, 1112864200, 2266587900, 4613409000, 9384609960, 19079454960
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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n*a(n) = 6*a(n-1) + 4*(n-2)*a(n-2) for n > 1.
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MAPLE
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seq(coeff(series((1/2)*(((1+2*x)/(1-2*x))^(3/2)-1), x, n+1), x, n), n=0..35); # Muniru A Asiru, Jun 06 2018
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MATHEMATICA
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CoefficientList[Series[((((1+2x)/(1-2x))^(3/2))-1)/2, {x, 0, 40}], x] (* Harvey P. Dale, Nov 04 2020 *)
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CROSSREFS
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1/2 * (((1 + 2*x)/(1 - 2*x))^(m/2) - 1): A001405(n-1) (m=1), this sequence (m=3).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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