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A081673
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Expansion of exp(3*x) - exp(x)*(1-BesselI_0(2*x)).
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4
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1, 3, 11, 33, 99, 293, 869, 2579, 7667, 22821, 68001, 202799, 605229, 1807263, 5399195, 16136513, 48243347, 144275093, 431573297, 1291258319, 3864163769, 11565703931, 34622195135, 103656406949, 310377872861, 929465445743
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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E.g.f. exp(3*x) - exp(x)*(1-BesselI_0(2*x)).
Conjecture: n*(2*n - 7)*a(n) +(-12*n^2 + 50*n - 33)*a(n-1) +(16*n^2 - 76*n + 87)*a(n-2) +3*(4*n^2 - 22*n + 27)*a(n-3) -9*(2*n-5)*(n-3)*a(n-4)=0. - R. J. Mathar, Nov 24 2012
E.g.f. A(x) satisfies
-27 A + (-63 x + 9) A' + (-18 x^2 + 42 x + 39) A'' + (12 x^2 + 68 x - 25) A''' + (16 x^2 - 58 x + 4) A'''' + (-12 x^2 + 11 x) A''''' + 2 x^2 A'''''' = 0.
This implies Mathar's conjectured recursion. (End)
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MAPLE
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Egf:= exp(3*x)-exp(x)*(1-BesselI(0, 2*x)):
S:= series(Egf, x, 101):
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MATHEMATICA
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CoefficientList[Series[E^(3*x)-E^x*(1-BesselI[0, 2*x]), {x, 0, 50}], x] * Range[0, 50]! (* Vaclav Kotesovec, Jul 02 2015 *)
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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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