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Search: id:A127846
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| A127846 |
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Series reversion of x/(1+5x+4x^2). |
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+0
2
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| 0, 1, 5, 29, 185, 1257, 8925, 65445, 491825, 3768209, 29324405, 231153133, 1841801065, 14810069497, 120029657805, 979470140661, 8040831465825, 66361595715105, 550284185213925, 4582462506008253, 38306388126997785
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Hankel transform is -A127847(n)=-4^C(n,2)*(4^n-1)/3; a(n+1) counts (5,4)-Motzkin paths of length n, where there are 5 colors available for the H(1,0) steps and 4 for the U(1,1) steps. See A059231 for more information.
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FORMULA
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G.f.: (1-5x-sqrt(1-10x+9x^2))/(8x); a(n)=sum{k=0..n-1, (1/n)*C(n,k)C(n,k+1)4^k}; a(n+1)=sum{k=0..floor(n/2), C(n, 2k)C(k)5^(n-2k)*4^k};
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CROSSREFS
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Sequence in context: A139174 A081336 A059231 this_sequence A137573 A078945 A113713
Adjacent sequences: A127843 A127844 A127845 this_sequence A127847 A127848 A127849
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Feb 02 2007
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