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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

%I

%S -1,3,-12,20,-45,63,-112,144,-225,275,-396,468,-637,735,-960,1088,

%T -1377,1539,-1900,2100,-2541,2783,-3312,3600,-4225,4563,-5292,5684,

%U -6525,6975,-7936,8448,-9537,10115,-11340,11988,-13357,14079,-15600,16400,-18081,18963,-20812,21780,-23805

%N G.f.: (1-2*x+6*x^2-2*x^3+x^4)/((x-1)^3*(x+1)^4).

%C 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

%C Unsigned = partial sums of positive integers of A129194. - _Omar E. Pol_, Aug 22 2011

%C Unsigned, see A212760. [_Clark Kimberling_, May 29 2012]

%D Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254.

%H Vincenzo Librandi, <a href="/A122576/b122576.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-1,3,3,-3,-3,1,1).

%F a(n) = n*(n+1)/8 * ((2*n+1)*(-1)^n - 1). - _Ralf Stephan_, Jan 01 2014

%F a(n) = (n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8. - _Wesley Ivan Hurt_, Jul 22 2014

%p a:=n->(sum(-(numbperm(n,2)), j=1..n/2)):seq(a(n)/2, n=2..46); # _Zerinvary Lajos_, Apr 12 2008

%p 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

%t 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}]

%t Table[(n + 1) (n + 2) (2 n + 3 + (-1)^n) (-1)^(n + 1)/8, {n, 0, 50}] (* _Wesley Ivan Hurt_, Jul 22 2014 *)

%t 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 *)

%o (MAGMA) [(n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8 : n in [0..50]]; // _Wesley Ivan Hurt_, Jul 22 2014

%Y Cf. A098023, A143120, A026741, A212760.

%K sign,easy

%O 1,2

%A _Roger L. Bagula_, Sep 17 2006

%E 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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Last modified September 15 22:10 EDT 2019. Contains 327088 sequences. (Running on oeis4.)