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%I #6 Aug 22 2017 16:22:06
%S 1,3,28,285,3324,41286,537528,7233633,99829180,1405109706,20092995624,
%T 291094349442,4263366676632,63021155618700,939010901406960,
%U 14088102521345865,212648697998549820,3226980657263323170,49203799749341113800,753450185890639113030
%N G.f. A(x) satisfies: x = A(x) * (1 + 2*A(x)) * (1 - 5*A(x)).
%F G.f.: Series_Reversion(x - 3*x^2 - 10*x^3).
%F a(n) ~ 2^(n - 3/2) * 3^(n - 3/4) * (54 + 13*sqrt(39))^(n - 1/2) / (13^(1/4) * sqrt(Pi) * n^(3/2) * 7^(2*n - 1)). - _Vaclav Kotesovec_, Aug 22 2017
%e G.f.: A(x) = x + 3*x^2 + 28*x^3 + 285*x^4 + 3324*x^5 + 41286*x^6 +...
%e Related expansions.
%e A(x)^2 = x^2 + 6*x^3 + 65*x^4 + 738*x^5 + 9142*x^6 + 118476*x^7 +...
%e A(x)^3 = x^3 + 9*x^4 + 111*x^5 + 1386*x^6 + 18210*x^7 + 246321*x^8 +...
%e where x = A(x) - 3*A(x)^2 - 10*A(x)^3.
%t Rest[CoefficientList[InverseSeries[Series[x - 3*x^2 - 10*x^3, {x, 0, 20}], x],x]] (* _Vaclav Kotesovec_, Aug 22 2017 *)
%o (PARI) {a(n)=polcoeff(serreverse(x - 3*x^2 - 10*x^3 +x^2*O(x^n)),n)}
%o for(n=1,30,print1(a(n),", "))
%K nonn
%O 1,2
%A _Paul D. Hanna_, Nov 28 2014
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