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 A009117 Expansion of e.g.f.: 1/2 + exp(-4*x)/2. 6
 1, -2, 8, -32, 128, -512, 2048, -8192, 32768, -131072, 524288, -2097152, 8388608, -33554432, 134217728, -536870912, 2147483648, -8589934592, 34359738368, -137438953472, 549755813888, -2199023255552, 8796093022208, -35184372088832, 140737488355328, -562949953421312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Ghislain R. Franssens, On a Number Pyramid Related to the Binomial, Deleham, Eulerian, MacMahon and Stirling number triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.4.1. Katarzyna Grygiel, Pawel M. Idziak and Marek Zaionc, How big is BCI fragment of BCK logic, arXiv preprint arXiv:1112.0643 [cs.LO], 2011. - N. J. A. Sloane, Feb 21 2012 INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 171 Index entries for linear recurrences with constant coefficients, signature (-4). FORMULA 1 followed by (-4)^n /2. E.g.f.: cos(x)^2 (even powers). a(n) = Sum_{k, 0<=k<=n} A086872(n,k)*(-3)^(n-k). - Philippe Deléham, Aug 17 2007 G.f. (2*x+1)/(1+4*x). - R. J. Mathar, Mar 08 2011 E.g.f.: 1/2 + exp(-4*x)/2 = (G(0)+1)/2 ; G(k) = 1 - 4*x/(2*k+1 - 2*x*(2*k+1)/(2*x - (k+1)/G(k+1))) ; (continued fraction). - Sergei N. Gladkovskii, Dec 20 2011 a(n) = (-1)^n * A081294(n). - Philippe Deléham, Mar 09 2014 MAPLE A009117:=n->`if`(n=0, 1, (-4)^n/2); seq(A009117(n), n=0..30); # Wesley Ivan Hurt, Mar 10 2014 MATHEMATICA With[{nn=30}, CoefficientList[Series[1/2+Exp[-4x]/2, {x, 0, nn}], x] Range[ 0, nn]!] (* or *) LinearRecurrence[{-4}, {1, -2}, 30] (* Harvey P. Dale, Apr 09 2015 *) PROG (PARI) x='x+O('x^100); Vec((1+2*x)/(1+4*x)) \\ Altug Alkan, Dec 21 2015 (MAGMA) m:=30; R:=PowerSeriesRing(Integers(), m); Coefficients(R!((2*x+1)/(1+4*x))); // G. C. Greubel, Jul 26 2018 CROSSREFS a(n) = (-1)^n * A004171(n-1). Sequence in context: A274524 A081294 A004171 * A160637 A183895 A228921 Adjacent sequences:  A009114 A009115 A009116 * A009118 A009119 A009120 KEYWORD sign,easy AUTHOR EXTENSIONS Signs added and formula corrected by Olivier Gérard, Mar 15 1997 More terms from Olaf Voß, Feb 13 2008 Definition corrected by Joerg Arndt, May 16 2011 STATUS approved

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Last modified October 15 05:56 EDT 2018. Contains 316202 sequences. (Running on oeis4.)