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 A369398 Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3) ). 1

%I #13 Feb 16 2024 09:54:16

%S 1,2,5,15,52,198,797,3322,14195,61848,273792,1228131,5570200,25501610,

%T 117694557,546983631,2557677780,12024345942,56801925455,269483935384,

%U 1283469626512,6134259516564,29412031039568,141434223863670,681939435678239,3296147009539144

%N Expansion of (1/x) * Series_Reversion( x / (1+x)^2 * (1-x^3) ).

%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(n+k,k) * binomial(2*n+2,n-3*k).

%F a(n) = (1/(n+1)) * [x^n] ( (1+x)^2 / (1-x^3) )^(n+1). - _Seiichi Manyama_, Feb 16 2024

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/(1+x)^2*(1-x^3))/x)

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

%Y Cf. A215340, A369297.

%Y Cf. A370213.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 22 2024

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Last modified June 15 09:53 EDT 2024. Contains 373407 sequences. (Running on oeis4.)