This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A122576 #54 Nov 03 2024 09:34:01
%S A122576 -1,3,-12,20,-45,63,-112,144,-225,275,-396,468,-637,735,-960,1088,
%T A122576 -1377,1539,-1900,2100,-2541,2783,-3312,3600,-4225,4563,-5292,5684,
%U A122576 -6525,6975,-7936,8448,-9537,10115,-11340,11988,-13357,14079,-15600,16400,-18081,18963,-20812,21780,-23805
%N A122576 Expansion of g.f.: -x*(1 - 2*x + 6*x^2 - 2*x^3 + x^4)/((1-x)^3*(1+x)^4).
%C A122576 Unsigned = row sums of triangle A143120 and Sum_{n>=1} n*A026741(n). - _Gary W. Adamson_, Jul 26 2008
%C A122576 Unsigned = partial sums of positive integers of A129194. - _Omar E. Pol_, Aug 22 2011
%C A122576 Unsigned, see A212760. - _Clark Kimberling_, May 29 2012
%D A122576 Roger G. Newton, Scattering Theory of Waves and Particles, McGraw Hill, 1966; p. 254.
%H A122576 Vincenzo Librandi, <a href="/A122576/b122576.txt">Table of n, a(n) for n = 1..1000</a>
%H A122576 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (-1,3,3,-3,-3,1,1).
%F A122576 a(n) = n*(n+1)/8 * ((2*n+1)*(-1)^n - 1). - _Ralf Stephan_, Jan 01 2014
%F A122576 a(n) = (n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8 (with offset of 0). - _Wesley Ivan Hurt_, Jul 22 2014
%F A122576 E.g.f.: -(1/8)*x*( (6 - 9*x + 2*x^2)*exp(-x) + (2+x)*exp(x) ). - _G. C. Greubel_, Nov 02 2024
%p A122576 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 A122576 Table[(n + 1) (n + 2) (2 n + 3 + (-1)^n) (-1)^(n + 1)/8, {n, 0, 50}] (* _Wesley Ivan Hurt_, Jul 22 2014 *)
%t A122576 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 A122576 (Magma) [(n+1)*(n+2)*(2*n+3+(-1)^n)*(-1)^(n+1)/8 : n in [0..50]]; // _Wesley Ivan Hurt_, Jul 22 2014
%o A122576 (SageMath)
%o A122576 def A122576(n): return n*(n+1)*((2*n+1)*(-1)^n - 1)//8
%o A122576 [A122576(n) for n in range(1,51)] # _G. C. Greubel_, Nov 02 2024
%Y A122576 Cf. A026741, A098023, A143120, A212760.
%K A122576 sign,easy
%O A122576 1,2
%A A122576 _Roger L. Bagula_, Sep 17 2006
%E A122576 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.