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Search: id:A069955
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| A069955 |
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Let W(n)=Prod(k=1,n,1-1/4k^2), the partial Wallis product ( lim n -> infinity W(n)=2/Pi ); then a(n)=numerator(W(n)). |
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+0
3
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| 1, 3, 45, 175, 11025, 43659, 693693, 2760615, 703956825, 2807136475, 44801898141, 178837328943, 11425718238025, 45635265151875, 729232910488125, 2913690606794775, 2980705490751054825
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Equivalently, denominators in partial products of the following approximation to Pi: Pi = Product_{n >= 1} 4*n^2/(4*n^2-1). Numerators are in A056982.
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REFERENCES
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O. J. Farrell and B. Ross, Solved Problems in Analysis, Dover, NY, 1971; p. 77.
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LINKS
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B. Gourevitch, L'univers de Pi
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FORMULA
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a(n)= numerator(W(n)) with W(n)=(2*n)!*(2*n+1)!/((2^n)*n!)^4.
W(n)=(2*n+1)*(binomial(2*n,n)/2^(2*n))^2 = (2*n+1)*(A001790(n)/A046161(n))^2 in lowest terms.
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CROSSREFS
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Not the same as A001902(n).
Cf. A056982.
W(n)=(3/4)*(A120995(n)/A120994(n)), n>=1.
Sequence in context: A071968 A093585 A062270 this_sequence A062346 A002682 A073595
Adjacent sequences: A069952 A069953 A069954 this_sequence A069956 A069957 A069958
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 27 2002
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