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A080243
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Signed super-Catalan or little Schroeder numbers.
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7
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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)
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OFFSET
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0,3
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COMMENTS
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REFERENCES
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I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 1983, Exercise 2.7.12.(b).
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LINKS
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FORMULA
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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
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MATHEMATICA
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CoefficientList[Series[(-1 + x + Sqrt[1 + 6 x + x^2]) /x / 4, {x, 0, 30}], x] (* Vincenzo Librandi, Aug 05 2013 *)
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PROG
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(PARI) x='x+O('x^66); Vec( (-1+x+sqrt(1+6*x+x^2))/x/4 ) \\ Joerg Arndt, Aug 15 2013
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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