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

%I #8 Nov 28 2023 08:39:37

%S 1,1,1,-5,-23,1,601,7771,26545,-401183,-6965999,-42828389,528611161,

%T 15543020065,141983039017,-2393449681349,-83586615493919,

%U -708151768946879,15447932991283105,635290179334026427,7146984268771158601,-162583738763505944639

%N E.g.f. satisfies A(x) = exp(x*A(-x^2)).

%F a(0) = 1; a(n) = (n-1)! * Sum_{k=0..floor((n-1)/2)} (-1)^k * (2*k+1) * a(k) * a(n-1-2*k) / (k! * (n-1-2*k)!).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=(i-1)!*sum(j=0, (i-1)\2, (-1)^j*(2*j+1)*v[j+1]*v[i-2*j]/(j!*(i-1-2*j)!))); v;

%Y Cf. A141369, A367722, A367723.

%Y Cf. A138292.

%K sign

%O 0,4

%A _Seiichi Manyama_, Nov 28 2023