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A098440
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Expansion of 1/sqrt(1-2x-59x^2).
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2
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1, 1, 31, 91, 1531, 7051, 88201, 520381, 5529091, 37734931, 365291101, 2721338401, 24972058981, 196231466341, 1746558487831, 14182492489651, 124085095556851, 1028416533153331, 8913996083549341, 74841905963166481, 645571197111115201
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OFFSET
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0,3
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COMMENTS
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9th binomial transform of 2^n*LegendreP(n,-4) Binomial transform of 1/sqrt(1-60x^2).
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LINKS
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FORMULA
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a(n) = sum{k=0..floor(n/2), binomial(n-k, k)*binomial(n, k)*15^k}.
D-finite with recurrence: n*a(n) = (2*n-1)*a(n-1) + 59*(n-1)*a(n-2). - Vaclav Kotesovec, Oct 15 2012
a(n) ~ sqrt(450+15*sqrt(15))*(1+2*sqrt(15))^n/(30*sqrt(Pi*n)). - Vaclav Kotesovec, Oct 15 2012
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MATHEMATICA
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CoefficientList[Series[1/Sqrt[1-2x-59x^2], {x, 0, 30}], x] (* Harvey P. Dale, Apr 25 2012 *)
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PROG
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(PARI) x='x+O('x^66); Vec(1/sqrt(1-2*x-59*x^2)) \\ Joerg Arndt, May 11 2013
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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