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Search: id:A001900
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| A001900 |
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Successive numerators of Wallis's approximation to pi/2 (unreduced). |
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+0
5
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| 1, 2, 4, 16, 64, 384, 2304, 18432, 147456, 1474560, 14745600, 176947200, 2123366400, 29727129600, 416179814400, 6658877030400, 106542032486400, 1917756584755200, 34519618525593600, 690392370511872000
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) = number of permutations of [n+1] all of whose non-initial left-to-right minima are at even positions in the permutation. For example, a(2) = 4 counts 123, 132, 213, 312. - David Callan (callan(AT)stat.wisc.edu), Jul 22 2008
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REFERENCES
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H.-D. Ebbinghaus et al., Numbers, Springer, 1990, p. 146.
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LINKS
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J. Sondow, A faster product for Pi and a new integral for ln(Pi/2)
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FORMULA
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... 2.2.4.4.6.6....2n.2n/1.3.3.5.5.7.7....(2n-1).(2n+1) ...
a(n) = 2^n * A010551(n) = 2^n * [n/2]! * [(n+1)/2]!. - R. Stephan, Mar 11 2004
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PROGRAM
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(PARI) a(n)=if(n<0, 0, prod(k=1, n, if(k%2, k+1, k)))
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CROSSREFS
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Cf. A000246.
Sequence in context: A106186 A155543 A151371 this_sequence A113247 A138870 A153992
Adjacent sequences: A001897 A001898 A001899 this_sequence A001901 A001902 A001903
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KEYWORD
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nonn,frac
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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