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A072020 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!). 2
1, 229, 207775, 472630861, 2148321709561, 17028146983530961, 214877019857456672479, 4044349155369603186936985, 108105412214943249140163409201, 3949854849387058592656207156530781 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
a(2)=3!*LaguerreL(3, 3,-1)=229, special value of associated Laguerre polynomial.
LINKS
M. Janjic, Some classes of numbers and derivatives, JIS 12 (2009) 09.8.3
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.
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}] (* Robert G. Wilson v, Jun 13 2002 *)
CROSSREFS
Cf. A072019.
Sequence in context: A332740 A178673 A028452 * A177826 A122269 A171666
KEYWORD
nonn
AUTHOR
Karol A. Penson, Jun 05 2002
EXTENSIONS
a(9) from Robert G. Wilson v, Jun 13 2002
STATUS
approved

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Last modified July 13 17:55 EDT 2024. Contains 374285 sequences. (Running on oeis4.)