%I #11 Aug 21 2023 08:23:23

%S 1,1,-1,-2,5,6,-30,-13,189,-56,-1188,1266,7194,-14377,-40183,135278,

%T 188773,-1151800,-503880,9109076,-3419924,-67220176,80390824,

%U 458183898,-998680470,-2794491329,10156144385,13919066170,-92250872385,-36047778330,769826420850,-339940775445

%N G.f. satisfies A(x) = 1 + x*A(x) / (1 + x*A(x))^2.

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

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

%Y Cf. A090192, A365086, A365087, A365088.

%Y Cf. A106510, A364735.

%K sign

%O 0,4

%A _Seiichi Manyama_, Aug 21 2023