This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A058006 Alternating factorials: 0! - 1! + 2! - ... + (-1)^n n! 10
 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; text; internal format)
 OFFSET 0,3 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 0..400 Eric Weisstein's MathWorld, Incomplete Gamma Function. 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)). - Max Alekseyev, Jul 05 2010 G.f.: G(0)/(1-x), where G(k)= 1 - (2*k + 1)*x/( 1 - 2*x*(k+1)/(2*x*(k+1) - 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, May 24 2013 0 = a(n)*(-a(n+1) + a(n+3)) + a(n+1)*(2*a(n+1) - 2*a(n+2) -a(n+3)) + a(n+2)*(a(n+2)) if n>=-1. - Michael Somos, Jan 28 2014 a(n) = exp(1)*Gamma(0,1) + (-1)^n*exp(1)*(n+1)!*Gamma(-n-1,1), where Gamma(a,x) is the upper incomplete Gamma function. - Vladimir Reshetnikov, Oct 29 2015 EXAMPLE a(5) = 0!-1!+2!-3!+4!-5! = 1-1+2-6+24-120 = -100. G.f. = 1 + 2*x^2 - 4*x^3 + 20*x^4 - 100*x^5 + 620*x^6 - 4420*x^7 + 35900*x^8 + ... MATHEMATICA a[ n_] := Sum[ (-1)^k k!, {k, 0, n}]; (* Michael Somos, Jan 28 2014 *) PROG (PARI) {a(n) = sum(k=0, n, (-1)^k * k!)}; /* Michael Somos, Jan 28 2014 */ (Haskell) a058006 n = a058006_list !! n a058006_list = scanl1 (+) a133942_list -- Reinhard Zumkeller, Mar 02 2014 CROSSREFS Cf. A000142, A003422, A005165, A153229 (absolute values), A136580. Partial sums of A133942. Sequence in context: A188326 A158094 A108879 * A153229 A013329 A102087 Adjacent sequences:  A058003 A058004 A058005 * A058007 A058008 A058009 KEYWORD easy,sign AUTHOR Henry Bottomley, Nov 13 2000 EXTENSIONS Corrections and more information from Michael Somos, Feb 19 2003 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 23 20:23 EST 2017. Contains 295141 sequences.