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Search: id:A087299
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| A087299 |
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Ratio of volume of n-dimensional ball to circumscribing n-cube is pi^[n/2] divided by a(n). |
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+0
2
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| 1, 1, 4, 6, 32, 60, 384, 840, 6144, 15120, 122880, 332640, 2949120, 8648640, 82575360, 259459200, 2642411520, 8821612800, 95126814720, 335221286400, 3805072588800, 14079294028800, 167423193907200, 647647525324800
(list; graph; listen)
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OFFSET
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0,3
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LINKS
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Eric Weisstein's World of Mathematics, Ball
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EXAMPLE
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The volume of sphere (3-ball) is 4/3*pi*r^3 and circumscribing 3-cube is 2^3*r^3 so ratio is pi/6 and a(3)=6.
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, n++; A=exp(x^2+x*O(x^n)); n!*polcoeff(A*(1+2*intformal(1/A)), n)/2) /* Michael Somos May 25 2004 */
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CROSSREFS
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Cf. A072345, A072346.
Sequence in context: A068720 A068402 A078250 this_sequence A164127 A071394 A137021
Adjacent sequences: A087296 A087297 A087298 this_sequence A087300 A087301 A087302
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KEYWORD
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nonn,easy
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AUTHOR
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Eric Weisstein (eric(AT)weisstein.com), Aug 31, 2003
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