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 A080243 Signed super-Catalan or little Schroeder numbers. 5
 1, -1, 3, -11, 45, -197, 903, -4279, 20793, -103049, 518859, -2646723, 13648869, -71039373, 372693519, -1968801519, 10463578353, -55909013009, 300159426963, -1618362158587, 8759309660445, -47574827600981, 259215937709463, -1416461675464871, 7760733824437545, -42624971294485657 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Row sums of triangle A080245. REFERENCES I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, Exercise 2.7.12.(b). LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 FORMULA G.f.: (-1+x+sqrt(1+6*x+x^2))/x/4. - Vladeta Jovovic, Sep 27 2003 Conjecture: (n+1)*a(n) +3*(2*n-1)*a(n-1) +(n-2)*a(n-2)=0. - R. J. Mathar, Nov 26 2012 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 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 G.f. A(x) satisfies: A(x) = (1 - 2*x*A(x)^2) / (1 - x). - Ilya Gutkovskiy, Jun 30 2020 MATHEMATICA CoefficientList[Series[(-1 + x + Sqrt[1 + 6 x + x^2]) /x / 4, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *) PROG (PARI) x='x+O('x^66); Vec( (-1+x+sqrt(1+6*x+x^2))/x/4 ) \\ Joerg Arndt, Aug 15 2013 CROSSREFS Cf. A001003, A080245. Sequence in context: A217889 A217890 A001003 * A151131 A151132 A200075 Adjacent sequences:  A080240 A080241 A080242 * A080244 A080245 A080246 KEYWORD sign AUTHOR Paul Barry, Feb 13 2003 STATUS approved

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Last modified April 11 05:49 EDT 2021. Contains 342886 sequences. (Running on oeis4.)