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A020923
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Expansion of (1-4*x)^(11/2).
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7
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1, -22, 198, -924, 2310, -2772, 924, 264, 198, 220, 308, 504, 924, 1848, 3960, 8976, 21318, 52668, 134596, 354200, 956340, 2641320, 7443720, 21360240, 62300700, 184410072, 553230216, 1680180656, 5160554872, 16015515120, 50181947376, 158639704608, 505664058438
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = (10395/64)*4^n*Gamma(-11/2+n)/(sqrt(Pi)*Gamma(1+n)). - Peter Luschny, Dec 14 2015
D-finite with recurrence: n*a(n) +2*(-2*n+13)*a(n-1)=0. - R. J. Mathar, Jan 17 2020
a(n) = (-4)^n*binomial(11/2, n).
Sum_{n>=0} 1/a(n) = 1124/1155 + 26*Pi/(3^8*sqrt(3)).
Sum_{n>=0} (-1)^n/a(n) = 56972276/54140625 - 52*log(phi)/(5^7*sqrt(5)), where phi is the golden ratio (A001622). (End)
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MAPLE
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A002423 := n -> (10395/64)*4^n*GAMMA(-11/2+n)/(sqrt(Pi)*GAMMA(1+n)):
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MATHEMATICA
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CoefficientList[Series[(1 - 4*x)^(11/2), {x, 0, 50}], x] (* G. C. Greubel, Feb 15 2017 *)
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PROG
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(PARI) my(x='x+O('x^50)); Vec((1-4*x)^(11/2)) \\ G. C. Greubel, Feb 15 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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