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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
OFFSET
0,2
LINKS
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
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<x>:=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 * A331407 A160637 A183895
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