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A090969
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a(n) = 1/Integral_{x=0..1} (x^5 - x^6)^n.
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4
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1, 42, 858, 15504, 265650, 4417686, 72068304, 1160068104, 18490100706, 292486494300, 4599035681526, 71963547329856, 1121519754006288, 17419158268943970, 269767427275060200, 4167406330765934256
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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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a(n) = 1/B(5*n+1,n+1) = (6*n+1)!/(n! * (5*n)!), where B(p,q) is Euler's beta function (basically identical with R. J. Mathar's comment). - Emeric Deutsch, Jun 29 2009
a(n) ~ 2^(6*n+1) * 3^(6*n+3/2) * sqrt(n) / (sqrt(Pi) * 5^(5*n+1/2)). - Vaclav Kotesovec, Aug 15 2017
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MAPLE
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seq(factorial(6*n+1)/(factorial(n)*factorial(5*n)), n = 0 .. 16); # Emeric Deutsch, Jun 29 2009
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MATHEMATICA
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Table[1/Beta[5*n+1, n+1], {n, 0, 20}] (* G. C. Greubel, Feb 03 2019 *)
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PROG
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(PARI) vector(20, n, n--; (6*n+1)!/(n!*(5*n)!)) \\ G. C. Greubel, Feb 03 2019
(Magma) [Factorial(6*n+1)/(Factorial(n)*Factorial(5*n)): n in [0..20]]; // G. C. Greubel, Feb 03 2019
(Sage) [1/beta(5*n+1, n+1) for n in range(20)] # G. C. Greubel, Feb 03 2019
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Al Hakanson (hawkuu(AT)excite.com), Feb 29 2004
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EXTENSIONS
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STATUS
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approved
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