VOOZH about

URL: https://oeis.org/A379868

⇱ A379868 - OEIS

login
A379868
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x)^2.
6
1, 0, 1, -1, 25, -101, 2281, -19895, 472305, -6760297, 177126121, -3578690435, 105341330953, -2743981145933, 91092111623241, -2888769295882111, 107832291781283809, -4009180998104138321, 167254334458983887689, -7105017992715364001147, 328862774630320838523321
OFFSET
0,5
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)!.
PROG
(PARI) a(n) = -n!*sum(k=0, n, (-2*n+k-1)^(n-k-1)*binomial(2*n, k)/(n-k)!);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jan 04 2025
STATUS
approved