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A035018
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One fifth of 9-factorial numbers.
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13
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1, 14, 322, 10304, 422464, 21123200, 1246268800, 84746278400, 6525463436800, 561189855564800, 53313036278656000, 5544555772980224000, 626534802346765312000, 76437245886305368064000, 10013279211106003216384000, 1401859089554840450293760000, 208877004343671227093770240000
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OFFSET
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1,2
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LINKS
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FORMULA
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5*a(n) = (9*n-4)(!^9) := Product_{j=1..n} (9*j-4).
E.g.f.: (-1+(1-9*x)^(-5/9))/5.
a(n) = (1/5) * 9^n * Pochhammer(n, 5/9).
a(n) = (9*n-4)*a(n-1). (End)
Sum_{n>=1} 1/a(n) = 5*(e/9^4)^(1/9)*(Gamma(5/9) - Gamma(5/9, 1/9)). (End)
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MATHEMATICA
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Rest[FoldList[Times, 1, 9*Range[20]-4]/5] (* Harvey P. Dale, May 22 2013 *)
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PROG
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(Magma) [n le 1 select 1 else (9*n-4)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(5/9, n)/5 for n in range(1, 40)] # G. C. Greubel, Oct 18 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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