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A268407
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Number of North-East lattice paths that do not bounce off the diagonal y = x to the right.
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4
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1, 2, 5, 15, 48, 160, 548, 1914, 6785, 24335, 88109, 321521, 1181039, 4362855, 16195747, 60379623, 225955264, 848432824, 3195394520, 12067450014, 45685766306, 173350890788, 659126407978, 2510942564760, 9582235262428, 36627111558850, 140214938146148
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OFFSET
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0,2
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COMMENTS
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This sequence is related to paired pattern P_2 in Pan and Remmel's link.
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LINKS
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FORMULA
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G.f.: 2 (-1 + f(x) + x)/(1 - f(x) + (-5 + f(x))*x), where f(x) = sqrt(1 - 4*x).
a(n):= Sum_{k=0..n}((k+1)*fib(k)*binomial(2*n-k,n-k))/(n+1) + C(n), where fib(n) - Fibonacci numbers, C(n) - Catalan numbers. - Vladimir Kruchinin, Feb 27 2016
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MATHEMATICA
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CoefficientList[Series[2 (-1 + Sqrt[1 - 4 x] + x) / (1 - Sqrt[1 - 4 x] + (-5 + Sqrt[1 - 4 x]) x), {x, 0, 33}], x] (* Vincenzo Librandi, Feb 04 2016 *)
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PROG
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(Maxima) a(n):=sum((k+1)*fib(k)*binomial(2*n-k, n-k), k, 0, n)/(n+1)+binomial(2*n, n)/(n+1); /* Vladimir Kruchinin, Feb 27 2016 */
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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