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G.f. satisfies A(x) = (1 - 9*x*A(x))^(1/3).
1

%I #12 Oct 22 2024 12:58:02

%S 1,-3,0,9,27,0,-324,-1215,0,18711,75816,0,-1301265,-5484996,0,

%T 100048689,431943435,0,-8192222064,-35942240565,0,700434986472,

%U 3108770417700,0,-61805774132388,-276711654879477,0,5586291123504300,25180760594032407,0,-514555201693265040

%N G.f. satisfies A(x) = (1 - 9*x*A(x))^(1/3).

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

%F G.f.: (1/x) * Series_Reversion( x/(1-9*x)^(1/3) ).

%F a(n) = 9^n * binomial(2*n/3 - 4/3,n)/(n+1).

%o (PARI) a(n) = 9^n*binomial(2*n/3-4/3, n)/(n+1);

%Y Cf. A104624.

%K sign,easy

%O 0,2

%A _Seiichi Manyama_, Oct 22 2024