A379868 E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x)^2.

1, 0, 1, -1, 25, -101, 2281, -19895, 472305, -6760297, 177126121, -3578690435, 105341330953, -2743981145933, 91092111623241, -2888769295882111, 107832291781283809, -4009180998104138321, 167254334458983887689, -7105017992715364001147, 328862774630320838523321

Offset: 0

Author

Seiichi Manyama, Jan 04 2025

Keywords

• sign

Crossrefs

Cf. A108919, A379871.

Cf. A377859, A379879.

Cf. A364982, A367866.

Programs

PARI

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

Formula

E.g.f.: sqrt( (1/x) * Series_Reversion( x / (exp(-x) + x)^2 ) ).

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