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%I #6 Feb 23 2022 10:48:37
%S 1,1,-1,-2,0,10,10,-60,-220,400,4200,2200,-90200,-290400,1892000,
%T 15796000,-24024000,-775676000,-1592492000,36509880000,240055640000,
%U -1435950560000,-23703057840000,7376731120000,2082346354000000,9478853472000000,-162472029808000000
%N a(0) = a(1) = 1; a(n) = -Sum_{k=0..n-2} binomial(n-2,k) * a(k) * a(n-k-2).
%F E.g.f. A(x) satisfies: A(x) = 1 + x - Integral( Integral A(x)^2 dx) dx.
%t a[0] = a[1] = 1; a[n_] := a[n] = -Sum[Binomial[n - 2, k] a[k] a[n - k - 2], {k, 0, n - 2}]; Table[a[n], {n, 0, 26}]
%Y Cf. A007558, A307374, A346078.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Feb 23 2022