A369014 - OEIS

%I #17 Jan 14 2024 08:54:09

%S 1,0,0,3,3,3,36,78,129,685,2043,4554,17233,57279,153045,509848,

%T 1724739,5117643,16445555,55165536,173225715,555899673,1847495415,

%U 5971507824,19333284247,63975307425,209807070669,685973054145,2269660792842,7501194321663,24725092907853

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

%H Seiichi Manyama, <a href="/A369014/b369014.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(3*n+k+2,k) * binomial(n-2*k-1,n-3*k).

%o (PARI) my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1-x^3/(1-x))^3)/x)

%o (PARI) a(n, s=3, t=3, u=-3) = 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. A369012, A369013.

%Y Cf. A054514, A369011.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Jan 11 2024