%I #10 Jan 02 2021 11:25:16
%S 1,1,2,4,8,16,32,65,138,316,792,2142,6052,17316,49160,137109,374650,
%T 1004848,2658192,6982424,18351272,48607148,130447416,355542916,
%U 983250704,2749502132,7738681064,21826783844,61484999000,172649101544
%N Revert transform of (1 - x + 2x^2 - x^3)/(1 + 2x^2).
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F Recurrence: 23*(n-2)*(n-1)*n*(2452*n^4 - 34960*n^3 + 189323*n^2 - 462197*n + 428952)*a(n) = 6*(n-2)*(n-1)*(68656*n^5 - 1081864*n^4 + 6762924*n^3 - 20914012*n^2 + 31827523*n - 18878553)*a(n-1) - 12*(n-2)*(88272*n^6 - 1611648*n^5 + 12190896*n^4 - 48980992*n^3 + 110413409*n^2 - 132553882*n + 66249909)*a(n-2) + 16*(63752*n^7 - 1387100*n^6 + 12908594*n^5 - 66715481*n^4 + 207163859*n^3 - 387112415*n^2 + 403580697*n - 181214694)*a(n-3) - 16*(n-4)*(n-2)*(19616*n^5 - 338528*n^4 + 2307676*n^3 - 7753912*n^2 + 12781431*n - 8182557)*a(n-4) + 128*(n-5)*(n-4)*(2*n - 11)*(2452*n^4 - 25152*n^3 + 99155*n^2 - 178623*n + 123570)*a(n-5). - _Vaclav Kotesovec_, Jan 02 2021
%t Rest[CoefficientList[InverseSeries[Series[x*(1 - x + 2x^2 - x^3)/(1 + 2x^2), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)
%K nonn
%O 1,3
%A _Olivier GĂ©rard_