%I #19 Jan 13 2024 10:45:29

%S 1,3,15,93,644,4769,36953,295867,2428373,20322566,172759032,

%T 1487632887,12948891408,113748663495,1007117650350,8978151790011,

%U 80519598139947,725976573163011,6576546244337046,59829384514916820,546375444906314661,5006934930385254672

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

%H Seiichi Manyama, <a href="/A368966/b368966.txt">Table of n, a(n) for n = 0..1000</a>

%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+k+1,k) * binomial(4*n-2*k+2,n-3*k).

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

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

%Y Cf. A368962, A368968.

%Y Cf. A368965.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2024