A369231 - OEIS

%I #12 Jan 17 2024 09:35:37

%S 1,1,2,7,26,98,385,1569,6556,27908,120624,528030,2336202,10430155,

%T 46930285,212597901,968833424,4438398734,20428750419,94424634294,

%U 438104297376,2039690282940,9526029685218,44617396906698,209526541600978,986339358246758,4653571637230839

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

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

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

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

%Y Cf. A366052, A369232.

%Y Cf. A369229.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Jan 17 2024