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A027872
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a(n) = Product_{i=1..n} (5^i - 1).
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18
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1, 4, 96, 11904, 7428096, 23205371904, 362560730628096, 28324694519589371904, 11064305472020078810628096, 21609960560733744406929189371904, 211034749490954911990173458030810628096
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OFFSET
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0,2
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COMMENTS
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Given probability p = 1/5^n that an outcome will occur at the n-th stage of an infinite process, then starting at n=1, 1 - a(n)/A109345(n+1) is the probability that the outcome has occurred at or before the n-th iteration. The limiting ratio is 1-A100222 ~ 0.2396672. - Bob Selcoe, Mar 01 2016
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LINKS
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FORMULA
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a(n) = 5^(binomial(n+1,2))*(1/5; 1/5)_{n}, where (a;q)_{n} is the q-Pochhammer symbol. - G. C. Greubel, Dec 23 2015
G.f.: Sum_{n>=0} 5^(n*(n+1)/2)*x^n / Product_{k=0..n} (1 + 5^k*x). - Ilya Gutkovskiy, May 22 2017
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MAPLE
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mul( 5^i-1, i=1..n) ;
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MATHEMATICA
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Table[Product[(5^k-1), {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jul 17 2015 *)
Join[{1}, FoldList[Times, 5^Range[10]-1]] (* Harvey P. Dale, Dec 28 2021 *)
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PROG
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(Magma) [1] cat [&*[ 5^k-1: k in [1..n] ]: n in [1..11]]; // Vincenzo Librandi, Dec 24 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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