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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: A281813 A063102 * A212760 A143268 A193558 A256131

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 November 24 00:27 EST 2017. Contains 295164 sequences.