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A098399
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a(n) = 3^n*binomial(2*n+1, n).
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5
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1, 9, 90, 945, 10206, 112266, 1250964, 14073345, 159497910, 1818276174, 20827527084, 239516561466, 2763652632300, 31979409030900, 370961144758440, 4312423307816865, 50227047938102310, 585982225944526950, 6846739692614999100, 80106854403595489470, 938394580156404305220
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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.: (1-sqrt(1-12*x))/(6*x*sqrt(1-12*x)).
E.g.f.: a(n) = n!* [x^n] exp(6*x)*(BesselI(0, 6*x) + BesselI(1, 6*x)). - Peter Luschny, Aug 25 2012
(n+1)*a(n) - 6*(2*n+1)*a(n-1) = 0. - R. J. Mathar, Nov 24 2012
Sum_{n>=0} 1/a(n) = 6/11 + 72*arcsin(1/(2*sqrt(3)))/(11*sqrt(11)).
Sum_{n>=0} (-1)^n/a(n) = 6/13 + 72*arcsinh(1/(2*sqrt(3)))/(13*sqrt(13)). (End)
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MAPLE
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Z:=(1-sqrt(1-3*z))*4^n/sqrt(1-3*z)/6: Zser:=series(Z, z=0, 32): seq(coeff(Zser, z, n), n=1..18); # Zerinvary Lajos, Jan 01 2007
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MATHEMATICA
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Table[3^n Binomial[2n+1, n], {n, 0, 20}] (* Harvey P. Dale, Mar 28 2012 *)
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PROG
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(SageMath) [3^n*binomial(2*n+1, n) for n in range(21)] # G. C. Greubel, Dec 27 2023
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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