%I #10 Jan 02 2021 11:27:35
%S 1,1,0,0,2,2,2,13,24,32,118,286,482,1328,3540,7091,17244,46138,103468,
%T 243164,633618,1515992,3582432,9101608,22481022,54065300,135345444,
%U 338668916,828680300,2063798632,5185819200,12855728210,32040478058
%N Revert transform of (-1 - x + 2*x^2 + x^3)/(-1 - 2*x + 2*x^2 + 2*x^3).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F Recurrence: 49*(n-2)*(n-1)*n*(5472068*n^6 - 130415472*n^5 + 1278176366*n^4 - 6590115561*n^3 + 18841403270*n^2 - 28306685157*n + 17450153622)*a(n) = 84*(n-2)*(n-1)*(5472068*n^7 - 138623574*n^6 + 1466623125*n^5 - 8372302765*n^4 + 27708502009*n^3 - 52720827917*n^2 + 52609246467*n - 20613937590)*a(n-1) - 4*(n-2)*(125857564*n^8 - 3502986112*n^7 + 41138973688*n^6 - 264794199220*n^5 + 1012269992878*n^4 - 2315031745255*n^3 + 2992407324252*n^2 - 1839115506195*n + 287602483140)*a(n-2) + 24*(158689972*n^9 - 4972223478*n^8 + 68107487148*n^7 - 534823526511*n^6 + 2650647401235*n^5 - 8587681283739*n^4 + 18160348646888*n^3 - 24126377976543*n^2 + 18229917354408*n - 5952357014400)*a(n-3) - 16*(n-5)*(153217904*n^8 - 4264504832*n^7 + 50601328517*n^6 - 334028015708*n^5 + 1339574258267*n^4 - 3334303068905*n^3 + 5014008744969*n^2 - 4145978438946*n + 1434163302504)*a(n-4) + 16*(n-6)*(n-5)*(120385496*n^7 - 2808947636*n^6 + 27353676848*n^5 - 143853926837*n^4 + 440026991168*n^3 - 779829326825*n^2 + 737613061944*n - 285407886960)*a(n-5) - 592*(n-7)*(n-6)*(n-5)*(5472068*n^6 - 97583064*n^5 + 708180026*n^4 - 2672123457*n^3 + 5518041083*n^2 - 5900764788*n + 2547989136)*a(n-6). - _Vaclav Kotesovec_, Jan 02 2021
%t Rest[CoefficientList[InverseSeries[Series[x*(-1 - x + 2*x^2 + x^3)/(-1 - 2*x + 2*x^2 + 2*x^3), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)
%K nonn
%O 1,5
%A _Olivier GĂ©rard_