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%I #12 Jun 13 2015 00:54:59
%S 1,1,2,6,13,31,69,153,332,712,1509,3169,6603,13669,28142,57674,117741,
%T 239587,486193,984353,1989056,4012636,8083717,16266181,32698903,
%U 65678221,131827874,264447198,530221357,1062664807,2129046429
%N Expansion of (4*x^4-5*x^3-x^2+3*x-1) / (2*x^5+3*x^4-4*x^3-3*x^2+4*x-1).
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3,-4,3,2).
%F a(n) = sum(k=0..n, ((k*n-1)*sum(i=0..n-k, 2^i*binomial(k+1,n-k-i)*binomial(k+i,k)*(-1)^(n-i+1)))/(k+1)).
%F G.f.: x*(x-1)*(4*x^3-x^2-2*x+1) / ( (-1+2*x)*(x^2+x-1)^2 ).
%t CoefficientList[Series[(4*x^4-5*x^3-x^2+3*x-1) / (2*x^5+3*x^4-4*x^3-3*x^2+4*x-1), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 15 2014 *)
%o (Maxima)
%o a(n):=sum(((k*n-1)*sum(2^i*binomial(k+1,n-k-i)*binomial(k+i,k)*(-1)^(n-i+1),i,0,n-k))/(k+1),k,0,n);
%K nonn,easy
%O 0,3
%A _Vladimir Kruchinin_, Mar 14 2014
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