A098662 E.g.f. BesselI(0,2*sqrt(3)*x) + BesselI(1,2*sqrt(3)*x)/sqrt(3).
1, 1, 6, 9, 54, 90, 540, 945, 5670, 10206, 61236, 112266, 673596, 1250964, 7505784, 14073345, 84440070, 159497910, 956987460, 1818276174, 10909657044, 20827527084, 124965162504, 239516561466, 1437099368796, 2763652632300
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..1855
Programs
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Maple
seq(binomial(n, floor(n/2))*3^floor(n/2),n=0..30); # Robert Israel, Aug 23 2019
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Mathematica
With[{nn=30},CoefficientList[Series[BesselI[0,2Sqrt[3]x]+ BesselI[1, 2Sqrt[3]x]/ Sqrt[3],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Oct 01 2013 *)
Formula
G.f.: 1/sqrt(1-12*x^2) + (1-sqrt(1-12*x^2))/(6*x*sqrt(1-12*x^2));
G.f.: (1 + 6*x - sqrt(1-12*x^2))/(6*x*sqrt(1-12*x^2));
a(n) = binomial(n, floor(n/2))*3^floor(n/2).
Conjecture: (n+1)*a(n) + 6(n-1)*a(n-1) - 12n*a(n-2) + 72*(2-n)*a(n-3) = 0. - R. J. Mathar, Dec 08 2011
Conjecture confirmed using the differential equation x*(6x+1)*(12*x^2-1) * g'(x) + (6*x-1)*(12*x^2+6*x+1)*g(x) + 2*x + 1 = 0 satisfied by the g.f. - Robert Israel, Aug 23 2019
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