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Search: id:A094941
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| A094941 |
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n! times coefficient of pi^[n/2] in volume of n-dimensional unit ball. |
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+0
1
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| 1, 2, 2, 8, 12, 64, 120, 768, 1680, 12288, 30240, 245760, 665280, 5898240, 17297280, 165150720, 518918400, 5284823040, 17643225600, 190253629440, 670442572800, 7610145177600, 28158588057600, 334846387814400, 1295295050649600
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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E.g.f. A(x) satisfies A'(x) = 2+2*x*A(x), A(0)=1.
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REFERENCES
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L. Badger, Generating the Measures of n-Balls, Amer. Math. Monthly, 107 (2000), pp. 256-258.
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FORMULA
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E.g.f.: exp(-x^2)(1+2*Integral_{t=0..x} exp(-t^2) dt). a(n)=(2n-2)a(n-2), if n>1.
a(n)a(n+1)=n!2^(n+1).
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EXAMPLE
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The volume of sphere is 4/3*pi*r^3 so 3!*4/3 = 8 = a(3).
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MATHEMATICA
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Table[If[OddQ[n], 2^n ((n - 1)/2)!, 2(n - 1)!/((n/2 - 1)!)], {n, 1, 25}] - Robert A. Russell (russell(AT)post.harvard.edu), May 07 2006
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PROGRAM
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(PARI) a(n)=local(A); if(n<0, 0, A=exp(x^2+x*O(x^n)); n!*polcoeff(A*(1+2*intformal(1/A)), n))
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CROSSREFS
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Cf. A087299.
Sequence in context: A026537 A089248 A006663 this_sequence A002785 A045686 A045677
Adjacent sequences: A094938 A094939 A094940 this_sequence A094942 A094943 A094944
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, May 24 2004
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