A367031 G.f. satisfies A(x) = 1 + x*A(x)^2 - x^2*A(x)^4.

1, 1, 1, -1, -10, -33, -55, 65, 842, 3230, 6137, -6631, -102166, -421705, -864225, 795615, 14526042, 63072042, 136736102, -102140350, -2256842380, -10210904245, -23195817445, 13298317815, 371005984450, 1740942920122, 4120912606657, -1666840127743

Offset

0,5

Links

Table of n, a(n) for n=0..27.

Formula

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

Prog

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

Crossrefs

Cf. A082582, A367032.

Cf. A006605.

Sequence in context: A255533 A067878 A067877 * A348427 A063160 A065149

Adjacent sequences: A367028 A367029 A367030 * A367032 A367033 A367034

Keyword

sign

Author

Seiichi Manyama, Nov 02 2023

Status

approved