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A058006
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Alternating factorials: 0! - 1! + 2! - ... + (-1)^n n!
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4
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1, 0, 2, -4, 20, -100, 620, -4420, 35900, -326980, 3301820, -36614980, 442386620, -5784634180, 81393657020, -1226280710980, 19696509177020, -335990918918980, 6066382786809020, -115578717622022980, 2317323290554617020, -48773618881154822980
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n) = (-1)^n n!+a(n-1) = A005165(n)(-1)^n+1.
a(n) = -(n-1)*a(n-1)+n*a(n-2), n>0.
E.g.f.: d/dx ((GAMMA(0,1)-GAMMA(0,1+x))*exp(1+x)). [From Max Alekseyev (maxale(AT)gmail.com), Jul 05 2010]
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EXAMPLE
| a(5) = 0!-1!+2!-3!+4!-5! = 1-1+2-6+24-120 = -100.
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PROG
| (PARI) a(n)=if(n<0, 0, sum(k=0, n, (-1)^k*k!))
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CROSSREFS
| Cf. A000142, A003422, A005165.
Sequence in context: A188326 A158094 A108879 * A153229 A013329 A102087
Adjacent sequences: A058003 A058004 A058005 * A058007 A058008 A058009
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KEYWORD
| easy,sign
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AUTHOR
| Henry Bottomley (se16(AT)btinternet.com), Nov 13 2000
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EXTENSIONS
| Corrections and more information from Michael Somos, Feb 19 2003
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