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%I #27 Jun 30 2020 16:25:02
%S 1,-1,3,-11,45,-197,903,-4279,20793,-103049,518859,-2646723,13648869,
%T -71039373,372693519,-1968801519,10463578353,-55909013009,
%U 300159426963,-1618362158587,8759309660445,-47574827600981,259215937709463,-1416461675464871,7760733824437545,-42624971294485657
%N Signed super-Catalan or little Schroeder numbers.
%C Row sums of triangle A080245.
%D I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, Exercise 2.7.12.(b).
%H Vincenzo Librandi, <a href="/A080243/b080243.txt">Table of n, a(n) for n = 0..300</a>
%F G.f.: (-1+x+sqrt(1+6*x+x^2))/x/4. - _Vladeta Jovovic_, Sep 27 2003
%F Conjecture: (n+1)*a(n) +3*(2*n-1)*a(n-1) +(n-2)*a(n-2)=0. - _R. J. Mathar_, Nov 26 2012
%F G.f.: 1 - x/(Q(0) + x) where Q(k) = 1 + k*(1+x) + x + x*(k+1)*(k+2)/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Mar 14 2013
%F a(n) ~ (-1)^n * sqrt(4+3*sqrt(2)) * (3+2*sqrt(2))^n /(4*sqrt(Pi)*n^(3/2)). - _Vaclav Kotesovec_, Aug 15 2013
%F G.f. A(x) satisfies: A(x) = (1 - 2*x*A(x)^2) / (1 - x). - _Ilya Gutkovskiy_, Jun 30 2020
%t CoefficientList[Series[(-1 + x + Sqrt[1 + 6 x + x^2]) /x / 4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 05 2013 *)
%o (PARI) x='x+O('x^66); Vec( (-1+x+sqrt(1+6*x+x^2))/x/4 ) \\ _Joerg Arndt_, Aug 15 2013
%Y Cf. A001003, A080245.
%K sign
%O 0,3
%A _Paul Barry_, Feb 13 2003
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