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A147625
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Octo-factorial numbers (4).
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6
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1, 5, 65, 1365, 39585, 1464645, 65909025, 3493178325, 213083877825, 14702787569925, 1132114642884225, 96229744645159125, 8949366251999798625, 903885991451979661125, 98523573068265783062625, 11527258048987096618327125, 1440907256123387077290890625
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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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a(n) = (-3)^n*Sum_{k=0..n} (8/3)^k*s(n+1,n+1-k), where s(n,k) are the Stirling numbers of the first kind, A048994. - Mircea Merca, May 03 2012
a(n) = Product_{k=0..n-1} (8*k+5).
a(n) = 8^n*Gamma(5/8 + n)/Gamma(5/8).
E.g.f: 1/(1 - 8*x)^(5/8). (End)
Sum_{n>=1} 1/a(n) = 1 + (1/2)*(e/2)^(1/8)*(Gamma(5/8) - Gamma(5/8, 1/8)). - Amiram Eldar, Dec 20 2022
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MAPLE
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seq(8^(n-1)*pochhammer(5/8, n-1), n = 1..20); # G. C. Greubel, Dec 03 2019
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MATHEMATICA
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PROG
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(PARI) vector(20, n, prod(j=0, n-2, 8*j+5) ) \\ G. C. Greubel, Dec 03 2019
(Magma) [Round(8^(n-1)*Gamma(n-1 +5/8)/Gamma(5/8)): n in [1..20]]; // G. C. Greubel, Dec 03 2019
(Sage) [8^(n-1)*rising_factorial(5/8, n-1) for n in (1..20)] # G. C. Greubel, Dec 03 2019
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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