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 A125695 Expansion of (sqrt(1+2x+9x^2)+x-1)/(2x). 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS First column of A125694. Hankel transform is (-2)^C(n+1, 2)*A001045(n+2). LINKS Table of n, a(n) for n=0..28. FORMULA 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 MATHEMATICA CoefficientList[Series[(Sqrt[1+2x+9x^2]+x-1)/(2x), {x, 0, 30}], x] (* Harvey P. Dale, Jul 25 2013 *) CROSSREFS Cf. A091593. Sequence in context: A268081 A319885 A368958 * A152681 A215603 A284563 Adjacent sequences: A125692 A125693 A125694 * A125696 A125697 A125698 KEYWORD easy,sign AUTHOR Paul Barry, Nov 30 2006, Dec 10 2008 STATUS approved

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Last modified May 22 11:36 EDT 2024. Contains 372755 sequences. (Running on oeis4.)