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A122576
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G.f.: (1 - 2*x + 6*x^2 - 2*x^3 + x^4)/((x-1)^3*(x+1)^4).
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4
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-1, 3, -12, 20, -45, 63, -112, 144, -225, 275, -396, 468, -637, 735, -960, 1088, -1377, 1539, -1900, 2100, -2541, 2783, -3312, 3600, -4225, 4563, -5292, 5684, -6525, 6975, -7936, 8448, -9537, 10115, -11340, 11988, -13357, 14079, -15600, 16400, -18081, 18963, -20812, 21780, -23805
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OFFSET
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1,2
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COMMENTS
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Unsigned = row sums of triangle A143120 and Sum_{n>=1} n*A026741(n). - Gary W. Adamson, Jul 26 2008
Unsigned = partial sums of positive integers of A129194. - Omar E. Pol, Aug 22 2011
Unsigned, see A212760. - Clark Kimberling, May 29 2012
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REFERENCES
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Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (-1,3,3,-3,-3,1,1).
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FORMULA
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a(n) = n*(n+1)/8 * ((2*n+1)*(-1)^n - 1). - Ralf Stephan, Jan 01 2014
a(n) = (n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8. - Wesley Ivan Hurt, Jul 22 2014
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MAPLE
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A122576:=n->(n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8: seq(A122576(n), n=0..50); # Wesley Ivan Hurt, Jul 22 2014
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MATHEMATICA
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Table[(n + 1) (n + 2) (2 n + 3 + (-1)^n) (-1)^(n + 1)/8, {n, 0, 50}] (* Wesley Ivan Hurt, Jul 22 2014 *)
CoefficientList[Series[(1 - 2 x + 6 x^2 - 2 x^3 + x^4)/((x - 1)^3 (x + 1)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 23 2014 *)
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PROG
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(Magma) [(n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8 : n in [0..50]]; // Wesley Ivan Hurt, Jul 22 2014
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CROSSREFS
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Cf. A098023, A143120, A026741, A212760.
Sequence in context: A344015 A281813 A063102 * A212760 A143268 A193558
Adjacent sequences: A122573 A122574 A122575 * A122577 A122578 A122579
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KEYWORD
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sign,easy
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AUTHOR
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Roger L. Bagula, Sep 17 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, May 20 2007. The simple generating function now used to define the sequence was found by an anonymous correspondent.
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STATUS
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approved
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