%I #7 Aug 27 2023 14:00:34
%S 1,1,2,5,19,90,510,3395,25831,221140,2104310,22027170,251540795,
%T 3111928820,41460769350,591847005749,9011786683883,145794610986004,
%U 2497443795363566,45157627509568965,859494143391347310,17176870199851102510,359623890969235361700
%N E.g.f.: -log( Sum_{n>=0} (-x)^(n^2) / (n^2)! ).
%e E.g.f.: A(x) = x + x^2/2! + 2*x^3/3! + 5*x^4/4! + 19*x^5/5! + 90*x^6/6! +...
%e where
%e exp(-A(x)) = 1 - x + x^4/4! - x^9/9! + x^16/16! - x^25/25! + x^36/36! +...
%o (PARI) {a(n) = n!*polcoeff(-log(sum(m=0, sqrtint(n+1), (-x)^(m^2)/(m^2)!+x*O(x^n))), n)}
%o for(n=1,25,print1(a(n),", "))
%Y Cf. A205802, A205803.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jan 31 2012