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A122576
G.f.: (1 - 2*x + 6*x^2 - 2*x^3 + x^4)/((x-1)^3*(x+1)^4).
4
-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
OFFSET
1,2
COMMENTS
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
REFERENCES
Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254.
FORMULA
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
MAPLE
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
MATHEMATICA
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 *)
PROG
(Magma) [(n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8 : n in [0..50]]; // Wesley Ivan Hurt, Jul 22 2014
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Roger L. Bagula, Sep 17 2006
EXTENSIONS
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.
STATUS
approved