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A005429
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Apéry numbers: n^3*C(2n,n).
(Formerly M2169)
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7
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0, 2, 48, 540, 4480, 31500, 199584, 1177176, 6589440, 35443980, 184756000, 938929992, 4672781568, 22850118200, 110079950400, 523521630000, 2462025277440, 11465007358860, 52926189069600, 242433164404200, 1102772230560000, 4984806175188840, 22404445765690560
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OFFSET
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0,2
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REFERENCES
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S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 1.6.3.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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FORMULA
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Sum_{n>=1} (-1)^(n+1) / a(n) = 2 * zeta(3) / 5.
G.f.: (2*x*(2*x*(2*x + 5) + 1))/(1-4*x)^(7/2). - Harvey P. Dale, Apr 08 2012
a(n) ~ 4^n*n^(5/2)/sqrt(Pi).
Sum_{n>=1} 1/a(n) = (1/2)*4F3(1,1,1,1; 3/2,2,2; 1/4) = A145438. (End)
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MATHEMATICA
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Table[n^3 Binomial[2n, n], {n, 0, 30}] (* Harvey P. Dale, Apr 08 2012 *)
CoefficientList[Series[(2*x*(2*x*(2*x+5)+1))/(1-4*x)^(7/2), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 22 2014 *)
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PROG
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(SageMath) [n^3*binomial(2*n, n) for n in range(31)] # G. C. Greubel, Nov 19 2022
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CROSSREFS
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KEYWORD
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nonn,nice,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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