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%I #8 Jan 01 2018 17:52:16
%S 0,1,-1,3,-15,85,-570,4509,-40804,414864,-4686570,58245650,-789691134,
%T 11598605460,-183459343613,3109122970590,-56203651969935,
%U 1079493501290439,-21953265755518782,471258656426134701,-10648683969964745520,252651472831081785300
%N E.g.f. equals the ratio of two power series, each with triangular exponents of x.
%C E.g.f. is asymptotic to 1-1/(2x). Compare to e.g.f. of A093523.
%H Robert Israel, <a href="/A093615/b093615.txt">Table of n, a(n) for n = 0..440</a>
%F E.g.f: T1(x)/T0(x), where T0(x) = sum_{n>=0} x^(n*(n+1)/2)/(n*(n+1)/2)! and T1(x) = sum_{n>=0} x^(n*(n+1)/2+1)/(n*(n+1)/2+1)!; T0(r)=0 at r=-0.8851021553904208809237177147294641529670...
%p N:= 10: # to get a(0)..a((N+1)*(N+2)/2-1)
%p T0:= add(x^(n*(n+1)/2)/(n*(n+1)/2)!, n=0..N):
%p T1:= add(x^(1+n*(n+1)/2)/(1+n*(n+1)/2)!,n=0..N):
%p S:= series(T1/T0,x,(N+1)*(N+2)/2):
%p seq(coeff(S,x,n)*n!,n=0..(N+1)*(N+2)/2-1); # _Robert Israel_, Jan 01 2018
%o (PARI) T0(x)=sum(k=0,sqrtint(2*n)+1,x^(k*(k+1)/2)/(k*(k+1)/2)!)
%o (PARI) T1(x)=sum(k=0,sqrtint(2*n)+1,x^(k*(k+1)/2+1)/(k*(k+1)/2+1)!)
%o (PARI) a(n)=n!*polcoeff(T1(x)/T0(x)+x*O(x^n),n)
%Y Cf. A093523.
%K sign
%O 0,4
%A _Paul D. Hanna_, Apr 05 2004
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