A386772 Expansion of (1/x) * Series_Reversion( x * (1-3*x) / (1+2*x)^2 ).

1, 7, 74, 943, 13326, 200982, 3169524, 51633343, 862145126, 14677296082, 253802667724, 4445613370118, 78712814985676, 1406483499289932, 25330499214488424, 459331317209458143, 8379478714912128726, 153679237018626276282, 2831839422052964444124

Offset: 0

Author

Seiichi Manyama, Aug 02 2025

Keywords

• nonn

Links

• Index entries for reversions of series

Crossrefs

Cf. A371391.

Programs

PARI

my(N=20, x='x+O('x^N)); Vec(serreverse(x*(1-3*x)/(1+2*x)^2)/x)

PARI

a(n) = sum(k=0, n, 2^k*3^(n-k)*binomial(2*(n+1), k)*binomial(2*n-k, n-k))/(n+1);

Formula

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

a(n) = (1/(n+1)) * [x^n] ( (1+2*x)^2 / (1-3*x) )^(n+1).