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A034977
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Expansion of 1/(1-64*x)^(1/8), related to octo-factorial numbers A045755.
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4
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1, 8, 288, 13056, 652800, 34467840, 1884241920, 105517547520, 6014500208640, 347504456499200, 20294260259553280, 1195516422562775040, 70933974405391319040, 4234212626044897198080, 254052757562693831884800
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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) = 8^n*A045755(n)/n!, n >= 1, A045755(n)=(8*n-7)!^8 := Product_{j=1..n} (8*j-7).
G.f.: (1-64*x)^(-1/8).
D-finite with recurrence: n*a(n) = 8*(8*n-7)*a(n-1). - R. J. Mathar, Jan 28 2020
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MATHEMATICA
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CoefficientList[Series[1/(1-64x)^(1/8), {x, 0, 30}], x] (* Harvey P. Dale, May 20 2011 *)
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PROG
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(Magma) [n le 1 select 8^(n-1) else 8*(8*n-15)*Self(n-1)/(n-1): n in [1..40]]; // G. C. Greubel, Oct 21 2022
(SageMath) [2^(6*n)*rising_factorial(1/8, n)/factorial(n) for n in range(40)] # G. C. Greubel, Oct 21 2022
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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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EXTENSIONS
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STATUS
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approved
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