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A035023
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One ninth of 9-factorial numbers.
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14
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1, 18, 486, 17496, 787320, 42515280, 2678462640, 192849310080, 15620794116480, 1405871470483200, 139181275577836800, 15031577762406374400, 1758694598201545804800, 221595519373394771404800, 29915395115408294139648000, 4307816896618794356109312000
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OFFSET
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1,2
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COMMENTS
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E.g.f. is g.f. for A001019(n-1) (powers of nine).
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LINKS
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FORMULA
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9*a(n) = (9*n)(!^9) = Product_{j=1..n} 9*j = 9^n*n!.
E.g.f.: (-1+1/(1-9*x))/9.
D-finite with recurrence: a(n) - 9*n*a(n-1) = 0. - R. J. Mathar, Jan 28 2020
Sum_{n>=1} 1/a(n) = 9*(exp(1/9)-1).
Sum_{n>=1} (-1)^(n+1)/a(n) = 9*(1-exp(-1/9)). (End)
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MATHEMATICA
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With[{nn=20}, Rest[CoefficientList[Series[(-1+1/(1-9*x))/9, {x, 0, nn}], x] Range[ 0, nn]!]] (* Harvey P. Dale, Apr 07 2019 *)
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PROG
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(Magma) [9^(n-1)*Factorial(n): n in [1..40]]; // G. C. Greubel, Oct 19 2022
(SageMath) [9^(n-1)*factorial(n) for n in range(1, 40)] # G. C. Greubel, Oct 19 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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STATUS
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approved
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