A049143 - OEIS

%I #10 Jan 02 2021 11:25:37

%S 1,1,2,4,10,26,74,219,678,2160,7062,23538,79734,273600,948972,3320845,

%T 11708586,41546434,148236556,531446460,1913357426,6914471176,

%U 25071324984,91181690872,332528253078,1215726924628,4454924130364

%N Revert transform of (1 - x - 2x^2 + x^3)/(1 - 2x^2 - 2x^3).

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F Recurrence: 49*(n-2)*(n-1)*n*(97276*n^6 - 3519516*n^5 + 45262750*n^4 - 283087617*n^3 + 934282738*n^2 - 1565876781*n + 1049863590)*a(n) = 84*(n-2)*(n-1)*(486380*n^7 - 18327150*n^6 + 254696367*n^5 - 1787076536*n^4 + 6991040383*n^3 - 15389861356*n^2 + 17672202225*n - 8109850050)*a(n-1) - 4*(n-2)*(23248964*n^8 - 934160180*n^7 + 14502686552*n^6 - 118351496900*n^5 + 565654855814*n^4 - 1636464877427*n^3 + 2810153593872*n^2 - 2619584037495*n + 1011295019700)*a(n-2) - 24*(1848244*n^9 - 80732634*n^8 + 1378035588*n^7 - 12765766611*n^6 + 72567277011*n^5 - 265962956799*n^4 + 632363275766*n^3 - 941709660585*n^2 + 794450752020*n - 286833522600)*a(n-3) + 16*(n-5)*(19455200*n^8 - 781724000*n^7 + 12160165721*n^6 - 99912786215*n^5 + 483488214059*n^4 - 1424023846157*n^3 + 2502350256972*n^2 - 2398791565710*n + 957442789080)*a(n-4) - 16*(n-6)*(n-5)*(11478568*n^7 - 409563604*n^6 + 5343328576*n^5 - 35012860513*n^4 + 127513525792*n^3 - 261159955705*n^2 + 280029420936*n - 121311223200)*a(n-5) + 304*(n-7)*(n-6)*(n-5)*(97276*n^6 - 2935860*n^5 + 29124310*n^4 - 135286257*n^3 + 322860367*n^2 - 382537080*n + 177022440)*a(n-6). - _Vaclav Kotesovec_, Jan 02 2021

%t Rest[CoefficientList[InverseSeries[Series[x*(1 - x - 2x^2 + x^3)/(1 - 2x^2 - 2x^3), {x, 0, 40}], x], x]] (* _Vaclav Kotesovec_, Jan 02 2021 *)

%K nonn

%O 1,3

%A _Olivier Gérard_