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 A239305 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). 0
 1, 1, 2, 6, 13, 31, 69, 153, 332, 712, 1509, 3169, 6603, 13669, 28142, 57674, 117741, 239587, 486193, 984353, 1989056, 4012636, 8083717, 16266181, 32698903, 65678221, 131827874, 264447198, 530221357, 1062664807, 2129046429 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Index entries for linear recurrences with constant coefficients, signature (4,-3,-4,3,2). FORMULA 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)). G.f.: x*(x-1)*(4*x^3-x^2-2*x+1) / ( (-1+2*x)*(x^2+x-1)^2 ). MATHEMATICA 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 *) PROG (Maxima) 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); CROSSREFS Sequence in context: A094687 A336875 A219753 * A018013 A263899 A062424 Adjacent sequences:  A239302 A239303 A239304 * A239306 A239307 A239308 KEYWORD nonn,easy AUTHOR Vladimir Kruchinin, Mar 14 2014 STATUS approved

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Last modified July 5 15:05 EDT 2022. Contains 355099 sequences. (Running on oeis4.)