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A276316
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G.f. A(x) satisfies: x = A(x)-4*A(x)^2+A(x)^3.
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4
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1, 4, 31, 300, 3251, 37744, 459060, 5773548, 74474455, 979872036, 13099102575, 177414673488, 2429310288468, 33574008073120, 467717206216760, 6560977611629676, 92595131510426943, 1313820730347196300, 18730821529411507725, 268185082351558093260
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Series_Reversion(x-4*x^2+x^3).
G.f. g(x) satisfies the differential equation
(12-184*t-27*t^2)*g''(t) - (92+27*t)*g'(t) + 3*g(t) = 4.
(-27*n^2+3)*a(n)+(-184*n^2-276*n-92)*a(n+1)+(12*n^2+36*n+24)*a(n+2) = 0
for n >= 1. (End)
a(n) ~ (46 + 13*sqrt(13))^(n - 1/2) / (13^(1/4) * sqrt(Pi) * n^(3/2) * 2^(n + 1/2) * 3^(n - 1/2)). - Vaclav Kotesovec, Aug 22 2017
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EXAMPLE
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G.f.: A(x) = x+4*x^2+31*x^3+300*x^4+3251*x^5+37744*x^6+459060*x^7+...
Related Expansions:
A(x)^2 = x^2+8*x^3+78*x^4+848*x^5+9863*x^6+120096*x^7+1511634*x^8+...
A(x)^3 = x^3+12*x^4+141*x^5+1708*x^6+21324*x^7+272988*x^8+3566761*x^9+...
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MAPLE
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S:= series(RootOf(x-4*x^2+x^3-t, x), t, 100):
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[x - 4*x^2 + x^3, {x, 0, 20}], x], x]] (* Vaclav Kotesovec, Aug 22 2017 *)
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PROG
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(PARI) {a(n)=polcoeff(serreverse(x - 4*x^2 + x^3 + x^2*O(x^n)), n)}
for(n=1, 30, print1(a(n), ", "))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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