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

0,5

Links

Table of n, a(n) for n=0..29.

Index entries for reversions of series

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).

Prog

(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);

Crossrefs

Cf. A370840, A370841.

Cf. A199874.

Sequence in context: A059859 A146617 A245240 * A203233 A112561 A303170

Adjacent sequences: A370836 A370837 A370838 * A370840 A370841 A370842

Keyword

sign

Author

Seiichi Manyama, Mar 03 2024

Status

approved