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Search: id:A097388
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| A097388 |
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2n-th derivative of the Gaussian exp(-x^2) evaluated at x=0. |
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+0
3
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| 1, -2, 12, -120, 1680, -30240, 665280, -17297280, 518918400, -17643225600, 670442572800, -28158588057600, 1295295050649600, -64764752532480000, 3497296636753920000, -202843204931727360000, 12576278705767096320000
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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E.g.f.: Sum_{k>=0} a(k)x^(2k)/(2k)! = exp(-x^2). a(n)=(-1)^n (2n)!/n!.
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EXAMPLE
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exp(-x^2) = 1 -x^2 +x^4/4 -x^6/6 +..., (d/dx)^4 exp(-x^2) = 12 -60x^2 +... so a(2)=12.
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (-1)^n*(2*n)!/n!)
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CROSSREFS
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a(n)=(-1)^n*A001813(n).
Sequence in context: A081470 A108135 A001813 this_sequence A152188 A131815 A047793
Adjacent sequences: A097385 A097386 A097387 this_sequence A097389 A097390 A097391
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 12 2004
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