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A125695
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Expansion of (sqrt(1+2x+9x^2)+x-1)/(2x).
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3
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1, 2, -2, -2, 10, -6, -42, 102, 82, -782, 814, 3854, -12454, -5014, 98694, -142218, -472158, 1932258, 19038, -14816994, 27370410, 64159962, -334154442, 121279878, 2418497010, -5523511086, -8914677362, 61259567662, -44249714438
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OFFSET
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0,2
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COMMENTS
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Hankel transform is (-2)^C(n+1, 2)*A001045(n+2).
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LINKS
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FORMULA
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a(n)=0^n+2*sum{k=0..floor((n-1)/2), C(n-1,2k)*C(k)*(-1)^(n-k-1)*2^k}, C(n)=A000108(n).
D-finite with recurrence: (n+1)*a(n) +(2*n-1)*a(n-1) +9*(n-2)*a(n-2)=0. - R. J. Mathar, Dec 02 2014
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MATHEMATICA
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CoefficientList[Series[(Sqrt[1+2x+9x^2]+x-1)/(2x), {x, 0, 30}], x] (* Harvey P. Dale, Jul 25 2013 *)
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CROSSREFS
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KEYWORD
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easy,sign
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AUTHOR
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STATUS
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approved
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