%I #10 Jan 02 2021 11:23:51
%S 1,1,2,6,20,70,254,947,3604,13936,54574,215914,861454,3461208,
%T 13988932,56821743,231793334,949033702,3897956648,16053912116,
%U 66275614190,274168532480,1136192222288,4715741791756,19598263084654
%N Revert transform of (1 - 3x + 2x^2 + x^3)/(1 - 2x + 2x^3).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F Recurrence: 23*(n-2)*(n-1)*n*(17172*n^6 - 423576*n^5 + 4356666*n^4 - 23917917*n^3 + 73913950*n^2 - 121852969*n + 83627530)*a(n) = 4*(n-2)*(n-1)*(1081836*n^7 - 28308042*n^6 + 315057411*n^5 - 1931263794*n^4 + 7030821771*n^3 - 15164709990*n^2 + 17878090855*n - 8840503650)*a(n-1) - 4*(n-2)*(3966732*n^8 - 113712984*n^7 + 1415715948*n^6 - 9998014698*n^5 + 43802809404*n^4 - 121878698873*n^3 + 210225001262*n^2 - 205376774691*n + 86927649480)*a(n-2) + 8*(2936412*n^9 - 94454586*n^8 + 1341241794*n^7 - 11038095603*n^6 + 58034133171*n^5 - 202174640931*n^4 + 466677806698*n^3 - 688129298199*n^2 + 587881625144*n - 221535308520)*a(n-3) - 16*(n-5)*(1184868*n^8 - 33966216*n^7 + 422624169*n^6 - 2983362075*n^5 + 13075866015*n^4 - 36449461159*n^3 + 63104412886*n^2 - 62005448370*n + 26439990552)*a(n-4) + 16*(n-6)*(n-5)*(618192*n^7 - 14939640*n^6 + 153479988*n^5 - 870020397*n^4 + 2941516152*n^3 - 5933206737*n^2 + 6606477556*n - 3125798560)*a(n-5) - 176*(n-7)*(n-6)*(n-5)*(17172*n^6 - 320544*n^5 + 2496366*n^4 - 10383573*n^3 + 24322015*n^2 - 30367004*n + 15720856)*a(n-6). - _Vaclav Kotesovec_, Jan 02 2021
%t Rest[CoefficientList[InverseSeries[Series[x*(1 - 3x + 2x^2 + x^3)/(1 - 2x + 2x^3), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)
%K nonn
%O 1,3
%A _Olivier GĂ©rard_