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A035017
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One quarter of 9-factorial numbers.
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13
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1, 13, 286, 8866, 354640, 17377360, 1007886880, 67528420960, 5132159992960, 436233599401600, 41005958343750400, 4223613709406291200, 473044735453504614400, 57238412989874058342400, 7440993688683627584512000, 1034298122727024234247168000, 153076122163599586668580864000
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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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4*a(n) = (9*n-5)(!^9) := Product_{j=1..n} (9*j-5).
E.g.f.: (-1+(1-9*x)^(-4/9))/4.
a(n) = (1/4) * 9^n * Pochhammer(n, 4/9).
a(n) = (9*n-5)*a(n-1). (End)
Sum_{n>=1} 1/a(n) = 4*(e/9^5)^(1/9)*(Gamma(4/9) - Gamma(4/9, 1/9)). (End)
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MATHEMATICA
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Table[9^n*Pochhammer[4/9, n]/4, {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-5)*Self(n-1): n in [1..40]]; // G. C. Greubel, Oct 18 2022
(SageMath) [9^n*rising_factorial(4/9, n)/4 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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