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A094893
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Total area below the lattice paths of length n defined by the rule [(0),(k)->(k-1)(k+1)] (Dyck paths).
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1
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1, 4, 12, 34, 84, 212, 488, 1162, 2580, 5932, 12888, 28948, 61992, 136936, 290256, 633178, 1331892, 2877308, 6016760, 12897340, 26843256, 57175384, 118545072, 251163204, 519103624, 1094915512, 2256939888, 4742198632, 9752832720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| Donatella Merlini, Generating functions for the area below some lattice paths, Discrete Mathematics and Theoretical Computer Science AC, 2003, 217-228
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LINKS
| D. Merlini, Generating functions for the area below some lattice paths
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FORMULA
| G.f.: (1+x-sqrt(1-4*x^2))/((1-2*x)*(1-4*x^2))
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MATHEMATICA
| CoefficientList[ Series[(1 + x - Sqrt[1 - 4*x^2])/((1 - 2*x)*(1 - 4*x^2)), {x, 0, 30}], x] (from Robert G. Wilson v Jun 15 2004)
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CROSSREFS
| Sequence in context: A000754 A119683 A135373 * A036880 A191823 A110335
Adjacent sequences: A094890 A094891 A094892 * A094894 A094895 A094896
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KEYWORD
| nonn,easy
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AUTHOR
| Donatella Merlini (merlini(AT)dsi.unifi.it), Jun 16 2004
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jun 16 2004
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