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%I #10 Aug 22 2023 07:56:59
%S 1,1,-2,1,6,-18,8,89,-266,62,1684,-4710,-220,35648,-91236,-34871,
%T 803302,-1856874,-1448844,18809694,-38816620,-48910700,451491680,
%U -820626294,-1522994404,11015923292,-17319046712,-45512957516,271664145264,-359911736252,-1327355044924
%N G.f. satisfies A(x) = 1 + x / (1 + x*A(x))^2.
%F If g.f. satisfies A(x) = 1 + x/(1 + x*A(x))^s, then a(n) = Sum_{k=0..n} (-1)^(n-k) * binomial(n-k+1,k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
%o (PARI) a(n, s=2) = sum(k=0, n, (-1)^(n-k)*binomial(n-k+1, k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
%Y Cf. A007440, A365110, A365111, A365112.
%Y Cf. A365085.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 22 2023