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A181768
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G.f.: (1/2)*(3 - sqrt((1-5*x)/(1-x))).
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3
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1, 1, 2, 5, 15, 51, 188, 731, 2950, 12235, 51822, 223191, 974427, 4302645, 19181100, 86211885, 390248055, 1777495635, 8140539950, 37463689775, 173164232965, 803539474345, 3741930523740, 17481709707825, 81912506777200, 384847173838501, 1812610804416698, 8556895079642921, 40480850291739165, 191884148712996795, 911225151259732188, 4334673398737025619, 20653004146207902678, 98551406393189773875
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OFFSET
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0,3
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COMMENTS
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Same as A007317 if the first 1 is omitted. Has several combinatorial interpretations so deserves its own entry.
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LINKS
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FORMULA
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D-finite with recurrence: n*a(n) +2*(-3*n+4)*a(n-1) +5*(n-2)*a(n-2)=0. - R. J. Mathar, Aug 06 2013
a(n) = JacobiP(n-1,1,-n-1/2,9)/n for n>0. - Peter Luschny, Sep 23 2014
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MAPLE
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A181768 := n -> `if`(n=0, 1, JacobiP(n-1, 1, -n-1/2, 9)/n):
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MATHEMATICA
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CoefficientList[Series[3/2-Sqrt[(1-5x)/(1-x)]/2, {x, 0, 40}], x] (* Harvey P. Dale, Jul 28 2013 *)
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PROG
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(PARI) x='x + O('x^50); Vec((1/2)*(3 - sqrt((1-5*x)/(1-x)))) \\ G. C. Greubel, Feb 12 2017
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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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