A368973 Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^2)^2 ).

1, 3, 13, 65, 351, 1989, 11650, 69903, 427225, 2649229, 16622079, 105310673, 672687322, 4327037010, 28002409452, 182179075689, 1190778886791, 7815755146095, 51491064226095, 340374137775879, 2256891800364421, 15006481967365535, 100037043223408890

Offset: 0

Author

Seiichi Manyama, Jan 10 2024

Keywords

• nonn

Links

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

Crossrefs

Cf. A368969, A368975.

Cf. A368965.

Programs

PARI

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

PARI

a(n, s=2, t=2, u=1) = 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(4*n-k+2,n-2*k).