A369630 - OEIS

%I #9 Jan 28 2024 09:19:38

%S 1,1,2,6,20,70,255,960,3707,14598,58395,236626,969275,4007041,

%T 16696822,70053159,295691622,1254772103,5349978803,22907982780,

%U 98466168572,424713570017,1837717336614,7974744620620,34698200181696,151341512079231,661590732178716

%N Expansion of (1/x) * Series_Reversion( x * (1/(1+x^3) - x) ).

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(2*n-3*k+1,k) * binomial(2*n-3*k,n-3*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1/(1+x^3)-x))/x)

%o (PARI) a(n) = sum(k=0, n\3, binomial(2*n-3*k+1, k)*binomial(2*n-3*k,n-3*k))/(n+1);

%Y Cf. A007863, A199874, A369631.

%Y Cf. A226974.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 28 2024