%I #12 Jan 02 2021 13:44:49
%S 1,1,2,6,22,90,392,1775,8252,39114,188220,916920,4512880,22406488,
%T 112092264,564474555,2859167178,14557198500,74459570756,382441401734,
%U 1971683051152,10199692593804,52927874586704,275432533945182
%N Revert transform of (1 - 3x + x^3)/(1 - 2x - 2x^2).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F Recurrence: 81*(n-2)*(n-1)*n*(2016*n^4 - 11424*n^3 - 46810*n^2 + 395773*n - 620517)*a(n) = 54*(n-2)*(n-1)*(32256*n^5 - 231168*n^4 - 544672*n^3 + 8226740*n^2 - 22221907*n + 18224505)*a(n-1) - 12*(n-2)*(471744*n^6 - 4560192*n^5 - 1059012*n^4 + 160656726*n^3 - 725097457*n^2 + 1289426626*n - 830096175)*a(n-2) + 24*(233856*n^7 - 3079104*n^6 + 6489976*n^5 + 96147244*n^4 - 733225467*n^3 + 2201910978*n^2 - 3131108227*n + 1741444400)*a(n-3) + 16*(n-4)*(14112*n^6 - 150528*n^5 - 79702*n^4 + 7934357*n^3 - 43412159*n^2 + 93807595*n - 72346950)*a(n-4) + 192*(n-5)*(n-4)*(2*n - 11)*(2016*n^4 - 3360*n^3 - 68986*n^2 + 275945*n - 280962)*a(n-5). - _Vaclav Kotesovec_, Jan 02 2021
%F a(n) ~ 3^(n - 1/2) * 4^(n-1) * sqrt(6 - sqrt(3*(3*2^(2/3) - 2 - 2^(4/3))) - sqrt(3*(-4 + 2^(4/3) - 3*2^(2/3) + 4*sqrt(3/(-2 - 2^(4/3) + 3*2^(2/3)))))) / (sqrt(Pi) * n^(3/2) * (2 + (-1 + sqrt(1 + 2^(1/3) + 2^(2/3)) - sqrt(2 - 2^(1/3) - 2^(2/3) + 2/sqrt(1 + 2^(1/3) + 2^(2/3))))^3)^n). - _Vaclav Kotesovec_, Jan 02 2021
%t Rest[CoefficientList[InverseSeries[Series[x*(1 - 3x + x^3)/(1 - 2x - 2x^2), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)
%K nonn
%O 1,3
%A _Olivier GĂ©rard_