%I #12 Jan 02 2021 13:29:44
%S 1,1,2,6,22,88,368,1585,6984,31348,142868,659434,3076432,14483556,
%T 68723800,328322903,1577959294,7624155960,37011662868,180436535308,
%U 883016392536,4336268255420,21361517691248,105535705919116
%N Revert transform of (-1 + 3x - 2x^2 + x^3)/(2x - 1).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F Recurrence: 23*(n-2)*(n-1)*n*(72*n^2 - 384*n + 485)*a(n) = 72*(n-2)*(n-1)*(216*n^3 - 1476*n^2 + 3183*n - 2171)*a(n-1) - 24*(n-2)*(1944*n^4 - 18144*n^3 + 61731*n^2 - 90333*n + 47597)*a(n-2) + 24*(2592*n^5 - 33264*n^4 + 166788*n^3 - 406284*n^2 + 477074*n - 213371)*a(n-3) - 48*(n-3)*(3*n - 13)*(3*n - 11)*(72*n^2 - 240*n + 173)*a(n-4). - _Vaclav Kotesovec_, Jan 02 2021
%F a(n) ~ (2*sqrt(3) - 3)^(1/4) * 2^(n - 3/2) * 3^(n-1) / (sqrt(Pi) * n^(3/2) * (3 - sqrt(2)*3^(1/4))^(n - 1/2)). - _Vaclav Kotesovec_, Jan 02 2021
%t Rest[CoefficientList[InverseSeries[Series[x*(-1 + 3x - 2x^2 + x^3)/(2x - 1), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)
%K nonn
%O 1,3
%A _Olivier GĂ©rard_