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A258723
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Expansion of 1/(1-12*x+48*x^2)^(1/2).
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2
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1, 6, 30, 108, 54, -3564, -41364, -314280, -1798362, -6972156, -1793340, 283697640, 3341429820, 25984971720, 151750943640, 596184213168, 101849014278, -25747257110940, -305001821608236, -2392882855430328, -14088646343199276, -55649498057805096, -7100681134947480
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OFFSET
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0,2
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LINKS
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FORMULA
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G.f.: 1/(1-12*x+48*x^2)^(1/2).
E.g.f.: exp(6*x)*BesselJ(0,2*sqrt(3)*x).
If mod(n,6)=4 then a(n) ~ (-1)^((n+8)/6) * 3^((n+1)/2) * 4^(n-1) / (sqrt(Pi) * n^(3/2)), else a(n) ~ 3^(n/2) * 2^(2*n+1) * cos(Pi*(n-1)/6) / sqrt(Pi*n). - Vaclav Kotesovec, Jun 08 2015
D-finite with recurrence n*a(n) +6*(-2*n+1)*a(n-1) +48*(n-1)*a(n-2)=0. [Belbachir]
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MATHEMATICA
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CoefficientList[Series[1/(1-12*x+48*x^2)^(1/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 08 2015 *)
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PROG
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(PARI) Vec(1/(1-12*x+48*x^2)^(1/2) + x^50) \\ G. C. Greubel, Feb 14 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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