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A035012
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One half of 9-factorial numbers.
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14
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1, 11, 220, 6380, 242440, 11394680, 638102080, 41476635200, 3069271004800, 254749493398400, 23436953392652800, 2367132292657932800, 260384552192372608000, 30985761710892340352000, 3966177498994219565056000, 543366317362208080412672000, 79331482334882379740250112000
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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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2*a(n) = (9*n-7)(!^9) := Product_{j=1..n} (9*j - 7).
E.g.f.: (-1+(1-9*x)^(-2/9))/2.
a(n) = (1/2) * 9^n * Pochhammer(n, 2/9).
a(n) = (9*n-7)*a(n-1). (End)
Sum_{n>=1} 1/a(n) = 2*(e/9^7)^(1/9)*(Gamma(2/9) - Gamma(2/9, 1/9)). (End)
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MATHEMATICA
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Table[9^n*Pochhammer[2/9, n]/2, {n, 40}] (* G. C. Greubel, Oct 18 2022 *)
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PROG
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(Magma) [n le 1 select 1 else (9*n-7)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(2/9, n)/2 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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