A370839 Expansion of (1/x) * Series_Reversion( x * (1/(1-x^2) - x) ).

1, 1, 1, 0, -5, -21, -59, -117, -96, 473, 3065, 10946, 27425, 39787, -46771, -598587, -2607973, -7726692, -15044242, -3990122, 123643981, 680120511, 2337866969, 5550672915, 6054525814, -23115014733, -181704066985, -726923651722, -2017980693299, -3365063873213

Offset: 0

Author

Seiichi Manyama, Mar 03 2024

Keywords

• sign

Links

• Index entries for reversions of series

Crossrefs

Cf. A370840, A370841.

Cf. A199874.

Programs

PARI

my(N=40, x='x+O('x^N)); Vec(serreverse(x*(1/(1-x^2)-x))/x)

PARI

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

Formula

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