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A009117
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E.g.f.: 1/2 + exp(-4*x)/2.
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6
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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; internal format)
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OFFSET
| 0,2
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COMMENTS
| E.g.f. cos(x)^2 (even powers).
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REFERENCES
| 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.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..200
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 171
Index to sequences with linear recurrences with constant coefficients, signature (-4).
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FORMULA
| 1 followed by (-4)^n /2.
a(n)=Sum_{k, 0<=k<=n} A086872(n,k)*(-3)^(n-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 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
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MATHEMATICA
| Cos[ x ]^2 (* Even Part *)
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CROSSREFS
| a(n) = (-1)^n*A004171(n-1).
Sequence in context: A099752 A081294 A004171 * A160637 A183895 A150829
Adjacent sequences: A009114 A009115 A009116 * A009118 A009119 A009120
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KEYWORD
| sign,easy
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AUTHOR
| R. H. Hardin (rhhardin(AT)att.net)
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EXTENSIONS
| Signs added and formula corrected Mar 15 1997 by Olivier Gerard.
More terms from Olaf Voss (richyfourtythree(AT)yahoo.com), Feb 13 2008
Corrected definition, Joerg Arndt, May 16 2011.
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