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%I #9 Jun 13 2015 00:51:47
%S 1,-1,1,-2,5,-10,15,-15,0,50,-175,450,-1000,2000,-3625,5875,-8125,
%T 8125,0,-29375,106250,-278125,621875,-1243750,2250000,-3640625,
%U 5031250,-5031250,0,18203125,-65859375,172421875,-385546875,771093750,-1394921875,2257031250,-3119140625,3119140625,0
%N Expansion of ((1+x)^4-(1+x)x^3)/((1+x)^5-x^5).
%C Binomial transform is A105367. Consecutive pair sums of 105369.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (-5,-10,-10,-5).
%F G.f.: (1+x)(1+3x+3x^2)/(1+5x+10x^2+10x^3+5x^4); a(n)=(5/2-sqrt(5)/2)^(n/2)((1/2+sqrt(5)/10)cos(7*pi*n/10)+ sqrt(1/10-sqrt(5)/50)sin(7*pi*n/10))- (5/2+sqrt(5)/2)^(n/2)((sqrt(5)/10-1/2)cos(9*pi*n/10)+sqrt(1/10+sqrt(5)/50)sin(9*pi*n/10))
%F a(0)=1, a(1)=-1, a(2)=1, a(3)=-2, a(n)=-5*a(n-1)-10*a(n-2)- 10*a(n-3)- 5*a(n-4) From _Harvey P. Dale_, May 23 2012
%t CoefficientList[Series[((1+x)^4-(1+x)x^3)/((1+x)^5-x^5),{x,0,40}],x] (* or *) LinearRecurrence[{-5,-10,-10,-5},{1,-1,1,-2},41] (* _Harvey P. Dale_, May 23 2012 *)
%K easy,sign
%O 0,4
%A _Paul Barry_, Apr 01 2005
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