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A079589
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a(n) = C(5n+1,n).
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2
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1, 6, 55, 560, 5985, 65780, 736281, 8347680, 95548245, 1101716330, 12777711870, 148902215280, 1742058970275, 20448884000160, 240719591939480, 2840671544105280, 33594090947249085, 398039194165652550
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OFFSET
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0,2
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COMMENTS
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a(n) is the number of paths from (0,0) to (5n,n) taking north and east steps while avoiding exactly 2 consecutive north steps. - Shanzhen Gao, Apr 15 2010
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REFERENCES
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Shanzhen Gao, Pattern Avoidance in Paths and Walks, in preparation [From Shanzhen Gao, Apr 15 2010]
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LINKS
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FORMULA
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a(n) is asymptotic to c*sqrt(n)*(3125/256)^n with c=0.557.... [c = 5^(3/2)/(sqrt(Pi)*2^(7/2)) = 0.55753878629774... - Vaclav Kotesovec, Feb 14 2019]
8*n*(4*n+1)*(2*n-1)*(4*n-1)*a(n) -5*(5*n+1)*(5*n-3)*(5*n-2)*(5*n-1)*a(n-1)=0. - R. J. Mathar, Jul 17 2014
G.f.: hypergeom([2/5, 3/5, 4/5, 6/5], [1/2, 3/4, 5/4], (3125/256)*x). - Robert Israel, Aug 07 2014
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MAPLE
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MATHEMATICA
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Table[Binomial[5n+1, n], {n, 0, 20}] (* Harvey P. Dale, Jan 23 2011 *)
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PROG
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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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