A368969 Expansion of (1/x) * Series_Reversion( x * (1-x+x^2)^2 ).

1, 2, 5, 12, 22, 0, -284, -1938, -9367, -36938, -118105, -260130, 56637, 4890560, 35945616, 186674620, 782890326, 2632462236, 5987222046, -2241224328, -129137211280, -967479390360, -5145272296080, -22060975744080, -75535676951124, -172915138783080

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..1000
• Index entries for reversions of series

Crossrefs

Cf. A368973, A368975.

Cf. A368961.

Programs

PARI

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

PARI

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

Formula

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