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Search: id:A077985
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| A077985 |
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Expansion of 1/(1+2*x-x^2). |
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+0
5
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| 1, -2, 5, -12, 29, -70, 169, -408, 985, -2378, 5741, -13860, 33461, -80782, 195025, -470832, 1136689, -2744210, 6625109, -15994428, 38613965, -93222358, 225058681, -543339720, 1311738121, -3166815962, 7645370045, -18457556052, 44560482149, -107578520350, 259717522849
(list; graph; listen)
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OFFSET
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0,2
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Tanya Khovanova, Recursive Sequences
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FORMULA
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a(n) = (-1)^n * A000129(n+1) [From M. F. Hasler (Maximilian.Hasler(AT)gmail.com), Oct 05 2008]
a(0)=1, a(1)=-2, a(n)=-2*a(n-1)+a(n-2) for n>1 . [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009]
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EXAMPLE
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sage: taylor( mul(x/(1 + 2*x - x^2) for i in xrange(1,2)),x,0,31)# solution: x - 2*x^2 + 5*x^3 - 12*x^4 + 29*x^5 - 70*x^6 + 169*x^7 - 408*x^8 + 985*x^9 - 2378*x^10 + 5741*x^11 - 13860*x^12 + 33461*x^13 - 80782*x^14 + 195025*x^15 - 470832*x^16 + 1136689*x^17 - 2744210*x^18 + 6625109*x^19 - 15994428*x^20 + 38613965*x^21 - 93222358*x^22 + 225058681*x^23 - 543339720*x^24 + 1311738121*x^25 - 3166815962*x^26 + 7645370045*x^27 - 18457556052*x^28 + 44560482149*x^29 - 107578520350*x^30 + 259717522849*x^31 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
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PROGRAM
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(Other) sage: taylor( mul(x/(1 + 2*x - x^2) for i in xrange(1, 2)), x, 0, 31)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 29 2009]
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CROSSREFS
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Essentially the same as A000129, which is the main entry for these numbers.
Sequence in context: A048624 A000129 A141682 this_sequence A054198 A054196 A131710
Adjacent sequences: A077982 A077983 A077984 this_sequence A077986 A077987 A077988
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2002
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