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 A024000 a(n) = 1 - n. 11
 1, 0, -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24, -25, -26, -27, -28, -29, -30, -31, -32, -33, -34, -35, -36, -37, -38, -39, -40, -41, -42, -43, -44, -45, -46, -47, -48, -49, -50, -51, -52, -53, -54, -55, -56 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is the weighted sum over all derangements (permutations with no fixed points) of n elements where each permutation with an odd number of cycles has weight +1 and each with an even number of cycles has weight -1. [Michael Somos, Jan 19 2011] LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA E.g.f.: (1-x)*exp(x). a(n) = Sum_{k=0..n} A094816(n,k)*(-1)^k (alternating row sums of Poisson-Charlier coefficient matrix). O.g.f.: (1-2*x)/(1-x)^2. a(n+1) = A001489(n). - R. J. Mathar, May 28 2008 a(n) = 2*a(n-1)-a(n-2) for n>1. - Wesley Ivan Hurt, Mar 02 2016 EXAMPLE a(4) = -3 because there are 6 derangements with one 4-cycle with weight -1 and 3 derangements with two 2-cycles with weight +1. - Michael Somos, Jan 19 2011 MAPLE A024000:=n->1-n: seq(A024000(n), n=0..100); # Wesley Ivan Hurt, Mar 02 2016 MATHEMATICA CoefficientList[Series[(1 - 2 x)/(1 - x)^2, {x, 0, 60}], x] Range[0, 60]! CoefficientList[Series[Exp[x] (1 - x), {x, 0, 60}], x] 1-Range[0, 60] (* Harvey P. Dale, Sep 18 2013 *) Flatten[NestList[(#/.x_/; x>1->Sequence[x, 2x])-1&, {1}, 60]] (* Robert G. Wilson v, Mar 02 2016 *) PROG (PARI) {a(n) = 1 - n} /* Michael Somos, Jan 19 2011 */ (MAGMA) [1-n: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011 CROSSREFS Cf. A000007, A000166, A087981, A137775. - Michael Somos, Jan 19 2011 Cf. A001489, A094816. Sequence in context: A056064 A274055 A167976 * A181983 A274922 A097141 Adjacent sequences:  A023997 A023998 A023999 * A024001 A024002 A024003 KEYWORD sign,easy AUTHOR STATUS approved

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Last modified November 13 17:16 EST 2018. Contains 317149 sequences. (Running on oeis4.)