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A072020
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Sum of an infinite series: a(n) = Sum_{ k = 0..infinity} ((1/27) * (3^n)^3 * GAMMA(n+1/3*k+1/3) * GAMMA(n+1/3*k+2/3) * GAMMA(n+1/3*k+1) / (GAMMA(4/3+1/3*k) * GAMMA(5/3+1/3*k) * GAMMA(2+1/3*k) * exp(1) * k!).
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2
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1, 229, 207775, 472630861, 2148321709561, 17028146983530961, 214877019857456672479, 4044349155369603186936985, 108105412214943249140163409201, 3949854849387058592656207156530781
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(2)=3!*LaguerreL(3, 3,-1)=229, special value of associated Laguerre polynomial.
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FORMULA
| Representation as n-th moment of a positive function on a positive half-axis, in Maple notation: a(n)=int(x^n*(exp(-x^(1/3))*BesselI(3, 2*x^(1/6))/(3*exp(1)*x^(7/6))), x=0..infinity), n=1, 2... This representation is unique.
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MATHEMATICA
| a[n_] := Sum[ 1/27*(3^n)^3 * Gamma[n + 1/3*k + 1/3] * Gamma[n + 1/3*k + 2/3] * Gamma[n + 1/3*k + 1] / Gamma[ 4/3 + 1/3*k] / Gamma[5/3 + 1/3*k] / Gamma[2 + 1/3*k] / Exp[1] / k!, {k, 0, Infinity}]
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CROSSREFS
| Cf. A072019.
Sequence in context: A124684 A178673 A028452 * A177826 A122269 A171666
Adjacent sequences: A072017 A072018 A072019 * A072021 A072022 A072023
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KEYWORD
| nonn
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AUTHOR
| Karol A. Penson (penson(AT)lptl.jussieu.fr), Jun 05 2002
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EXTENSIONS
| Mathematica code and a(9) from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 13 2002
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