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%I #8 Aug 27 2023 14:01:49
%S 1,1,3,10,44,249,1693,13384,120932,1229759,13894429,172677450,
%T 2341111850,34385290940,543885462121,9217332132024,166621796893824,
%U 3200275345024464,65082833538054240,1397097303096855578,31569176387677926733,749012642530028865010
%N E.g.f.: -log( Sum_{n>=0} (-x)^(n*(n+1)/2) / (n*(n+1)/2)! ).
%e E.g.f.: A(x) = x + x^2/2! + 3*x^3/3! + 10*x^4/4! + 44*x^5/5! + 249*x^6/6! +...
%e where
%e exp(-A(x)) = 1 - x - x^3/3! + x^6/6! + x^10/10! - x^15/15! - x^21/21! +...
%o (PARI) {a(n) = n!*polcoeff(-log(sum(m=0, sqrtint(2*n+1), (-x)^(m*(m+1)/2)/(m*(m+1)/2)!+x*O(x^n))), n)}
%o for(n=1,25,print1(a(n),", "))
%Y Cf. A205804.
%K nonn
%O 1,3
%A _Paul D. Hanna_, Jan 31 2012
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