A097388 - OEIS

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A097388

2n-th derivative of the Gaussian exp(-x^2) evaluated at x=0.

1, -2, 12, -120, 1680, -30240, 665280, -17297280, 518918400, -17643225600, 670442572800, -28158588057600, 1295295050649600, -64764752532480000, 3497296636753920000, -202843204931727360000, 12576278705767096320000 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,2`
	FORMULA	`E.g.f.: Sum_{k>=0} a(k)x^(2k)/(2k)! = exp(-x^2). a(n)=(-1)^n (2n)!/n!.`
	EXAMPLE	`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.`
	PROG	`(PARI) a(n)=if(n<0, 0, (-1)^n(2n)!/n!)`
	CROSSREFS	`a(n)=(-1)^nA001813(n).` `Sequence in context: A081470 A108135 A001813 A131815 A177774 A047793` `Adjacent sequences: A097385 A097386 A097387 * A097389 A097390 A097391`
	KEYWORD	`sign`
	AUTHOR	`Michael Somos, Aug 12 2004`

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Last modified February 15 19:15 EST 2012. Contains 205852 sequences.