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G.f. satisfies A(x) = (1 - 9*x*A(x))^(2/3).
0

%I #12 Oct 22 2024 12:57:59

%S 1,-6,27,-90,189,0,-1782,6318,0,-90882,360126,0,-5985819,24931800,0,

%T -446371074,1912892355,0,-35840971530,156454458930,0,-3022929941616,

%U 13367712796110,0,-264079216747476,1179032268616902,0,-23685874363658232,106533987128598645,0

%N G.f. satisfies A(x) = (1 - 9*x*A(x))^(2/3).

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

%F G.f.: (1/x) * Series_Reversion( x/(1-9*x)^(2/3) ).

%F a(n) = 9^n * binomial(n/3 - 5/3,n)/(n+1).

%o (PARI) a(n) = 9^n*binomial(n/3-5/3, n)/(n+1);

%Y Cf. A377268.

%K sign,easy

%O 0,2

%A _Seiichi Manyama_, Oct 22 2024