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A152029
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a(n) = 2^n*(2*n)!/((n+1)!).
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3
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1, 2, 16, 240, 5376, 161280, 6082560, 276756480, 14760345600, 903333150720, 62412108595200, 4805732361830400, 408117579035443200, 37896632339005440000, 3819980539771748352000, 415422883700177633280000, 48482294191832495554560000, 6044126009248451112468480000
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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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G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 2*x/(2*x + (k+2)/((2*k+1)*(2*k+2))/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 03 2013
4*(n+1)*(2*n+1)*a(n) = (n+2)*a(n+1). - Robert Israel, Jan 25 2017
E.g.f.: 1/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - 2*x/(1 - ...)))))), a continued fraction. - Ilya Gutkovskiy, May 10 2017
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MAPLE
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MATHEMATICA
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With[{nn=20}, CoefficientList[Series[2/(1+(1-8x)^(1/2)), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Mar 11 2023 *)
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PROG
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(Magma) [2^n*Factorial(2*n)/Factorial(n+1): n in [0..20]]; // Vincenzo Librandi, Jan 27 2017
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CROSSREFS
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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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