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Search: id:A123900
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| A123900 |
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(n+3)!/(d(n)*d(n+1)*d(n+2)) where d(n) = cancellation factor in reducing Sum_{k=0...n} 1/k! to lowest terms. |
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8
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| 6, 12, 60, 180, 2520, 1008, 18144, 18144, 3991680, 5987520, 155675520, 1089728640, 26153487360, 523069747200, 17784371404800, 12312257126400, 935731541606400, 4678657708032, 12772735542927360, 140500090972200960
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality, Amer. Math. Monthly 113 (2006) 637-641.
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LINKS
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J. Sondow, A geometric proof that e is irrational and a new measure of its irrationality
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FORMULA
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(n+3)!/(A093101(n)*A093101(n+1)*A093101(n+2)) where A093101(n) = GCD(n!,1+n+n(n-1)+...+n!)
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EXAMPLE
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a(2) = 60 because (2+3)!/(d(2)*d(3)*d(4)) =
5!/(GCD(2,5)*GCD(6,16)*GCD(24,65)) = 120/2 = 60.
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MATHEMATICA
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(A[n_] := If[n==0, 1, n*A[n-1]+1]; d[n_] := GCD[A[n], n! ]; Table[(n+3)!/(d[n]*d[n+1]*d[n+2]), {n, 0, 21}])
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CROSSREFS
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Cf. A000522, A061354, A093101, A123899, A123901.
Sequence in context: A093901 A117762 A104362 this_sequence A103972 A121735 A070970
Adjacent sequences: A123897 A123898 A123899 this_sequence A123901 A123902 A123903
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KEYWORD
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easy,nonn
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AUTHOR
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Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Oct 18 2006
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