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Search: id:A072346
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| A072346 |
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Volume of n-dimensional sphere of radius r is V_n*r^n = Pi^(n/2)*r^n/(n/2)! = C_n*Pi^floor(n/2)*r^n; sequence gives denominator of C_n. |
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13
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| 1, 1, 1, 3, 2, 15, 6, 105, 24, 945, 120, 10395, 720, 135135, 5040, 2027025, 40320, 34459425, 362880, 654729075, 3628800, 13749310575, 39916800, 316234143225, 479001600, 7905853580625, 6227020800, 213458046676875, 87178291200, 6190283353629375, 1307674368000
(list; graph; listen)
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OFFSET
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0,4
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COMMENT
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Answer to question of how to extend the sequence 1, 2 r, Pi r^2, 4 Pi r^3 / 3, Pi^2 r^4 / 2, ...
Surface area of n-dimensional sphere of radius r is n*V_n*r^(n-1).
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REFERENCES
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J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 9, Eq. 17.
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LINKS
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Eric Weisstein's World of Mathematics, Hypersphere
Eric Weisstein's World of Mathematics, Ball
Eric Weisstein's World of Mathematics, Four-Dimensional Geometry
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FORMULA
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(n/2)! if n even, n!! if n odd.
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EXAMPLE
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Sequence of C_n's begins 1, 2, 1, 4/3, 1/2, 8/15, 1/6, 16/105, 1/24, 32/945, 1/120, 64/10395, ...
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MATHEMATICA
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f[n_] := Pi^(n/2 - Floor[n/2])/(n/2)!; Table[ Denominator[ f[n]], {n, 0, 30} ]
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CROSSREFS
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Cf. A072345.
Cf. A001147.
Sequence in context: A033314 A070260 A142705 this_sequence A103236 A141235 A051917
Adjacent sequences: A072343 A072344 A072345 this_sequence A072347 A072348 A072349
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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), Jul 31 2002
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