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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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Unsigned = row sums of triangle A143120 and sum(n>=1, n*A026741(n) ); where A026741 = (1, 1, 3, 2, 5, 3, 7, 4, 9,...). - 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. LINKS 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). 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 a:=n->(sum(-(numbperm(n, 2)), j=1..n/2)):seq(a(n)/2, n=2..46); # Zerinvary Lajos, Apr 12 2008 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 gm = {{0, 1}, {1, 0}}; k = {{0, 1}, {1, 1}}; y[0] = {{0, 1}, {1, 1}}; y[n_] := y[n] = k*y[n - 1] + k*(y[n - 1][[1, 1]] + y[n - 1][[2, 2]])/n a = Table[Det[Sum[MatrixPower[gm, m].y[m], {m, 0, n}]], {n, 0, 25}] 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 Cf. A098023, A143120, A026741, A212760. Sequence in context: A063244 A281813 A063102 * A212760 A143268 A193558 Adjacent sequences:  A122573 A122574 A122575 * A122577 A122578 A122579 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

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Last modified December 1 06:09 EST 2020. Contains 338833 sequences. (Running on oeis4.)