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 A049145 Revert transform of (1 + x - x^3)/(1 + 2x + 2x^2). 0

%I #10 Jan 02 2021 11:26:23

%S 1,1,2,4,10,26,72,205,600,1790,5428,16676,51800,162408,513288,1633543,

%T 5230506,16838080,54465356,176933606,577002976,1888274740,6199187904,

%U 20411160754,67384417204,223006818992,739711312416,2458778309456

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

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

%F Recurrence: 23*(n-2)*(n-1)*n*(1952*n^4 - 27296*n^3 + 143698*n^2 - 337909*n + 300105)*a(n) = 6*(n-2)*(n-1)*(15616*n^5 - 241792*n^4 + 1475664*n^3 - 4388916*n^2 + 6235155*n - 3244875)*a(n-1) + 12*(n-2)*(19520*n^6 - 351040*n^5 + 2595700*n^4 - 10118262*n^3 + 21981753*n^2 - 25301906*n + 12089085)*a(n-2) - 8*(7808*n^7 - 167744*n^6 + 1499720*n^5 - 7198988*n^4 + 19849331*n^3 - 30868184*n^2 + 24125019*n - 6602040)*a(n-3) + 16*(n-4)*(n-2)*(1952*n^5 - 33152*n^4 + 232690*n^3 - 818047*n^2 + 1375383*n - 825255)*a(n-4) + 64*(n-5)*(n-4)*(2*n - 11)*(1952*n^4 - 19488*n^3 + 73522*n^2 - 124593*n + 80550)*a(n-5). - _Vaclav Kotesovec_, Jan 02 2021

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

%K nonn

%O 1,3