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Paul D. Hanna, <a href="/A341963/b341963_1.txt">Table of n, a(n) for n = 0..520</a>
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Paul D. Hanna, <a href="/A341963/b341963_1.txt">Table of n, a(n) for n = 0..520</a>
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a(n) ~ sqrt(s*(3 - 14*r*s + 15*r^2*s^2) / (Pi*(11 - 15*r*s))) / (2*n^(3/2)*r^(n + 1/2)), where r = 0.07627811703169412709742160523783922642030319519275992338... and s = 1.9374927720056356430894528816479641920545157312336620520408... are positive real roots of the system of equations (-1 + r*s)*(-1 + 2*r*s)/(1 - 3*r*s)^2 = s, -1 + 27*r^3*s^3 + r*(3 + 9*s) - r^2*s*(5 + 27*s) = 0. - Vaclav Kotesovec, Mar 02 2021
CoefficientList[1/x * InverseSeries[Series[x*(1 - 3*x)^2 / ((1 - x)*(1 - 2*x)), {x, 0, 20}], x], x] (* Vaclav Kotesovec, Mar 02 2021 *)
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AB(x)*BC(x) = D(x) + x*D(x)^2 = 1 + 97*x + 8359*x^2 + 810550*x^3 + 82705462*x^4 + 8738156651*x^5 + 947983606487*x^6 + 105009306651406*x^7 + 11828857474345054*x^8 + ...
BA(x)*CB(x) = D(x) + 3*x*D(x)^2 = 1 + 79*x + 5983*x^2 + 550810*x^3 + 54628270*x^4 + 5665187381*x^5 + 606487947983*x^6 + 665140610500930*x^7 + 74345054118288574*x^8 + ...
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{c(n) = my(A C = 1/x*serreverse( x*(1 - 3*x)^2 / ((1 - x)*(1 - 2*x) +x*O(x^n)))); polcoeff(A, C, n)}
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