A105369 Expansion of ((1+x)^3 - x^3)/((1+x)^5 - x^5).

1, -2, 3, -5, 10, -20, 35, -50, 50, 0, -175, 625, -1625, 3625, -7250, 13125, -21250, 29375, -29375, 0, 106250, -384375, 1006250, -2250000, 4500000, -8140625, 13171875, -18203125, 18203125, 0, -65859375, 238281250, -623828125, 1394921875, -2789843750, 5046875000, -8166015625

Offset: 0

Author

Paul Barry, Apr 01 2005

Keywords

• easy
• sign

Comments

Consecutive pair sums gives A105370.

Links

• Index entries for linear recurrences with constant coefficients, signature (-5,-10,-10,-5)

Formula

G.f.: (1 + 3*x + 3*x^2)/(1 + 5*x + 10*x^2 + 10*x^3 + 5*x^4);

a(n) = 2*sqrt(5)*(5/2 - sqrt(5)/2)^(n/2)*cos(7*Pi*n/10 + Pi/5)/5 + 2*sqrt(5)*(5/2 + sqrt(5)/2)^(n/2)*cos(9*Pi*n/10 + 2*Pi*/5)/5.