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A304944
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a(0) = 0, a(1) = 1 and a(n) = 6*a(n-1)/(n-1) + 16*a(n-2) for n > 1.
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2
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0, 1, 6, 34, 164, 790, 3572, 16212, 71048, 312678, 1345220, 5809980, 24692600, 105305980, 443684360, 1875046120, 7848968208, 32944100998, 137210821092, 572842556332, 2376270786840, 9878362137364, 40842721771544, 169192718317336, 697620779210096
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OFFSET
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0,3
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COMMENTS
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Let a(0) = 0, a(1) = 1 and a(n) = 2*m*a(n-1)/(n-1) + k^2*a(n-2) for n > 1, then the g.f. is x/(2*m) * d/dx ((1 + k*x)/(1 - k*x))^(m/k).
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LINKS
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FORMULA
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G.f.: x/(1-4*x)^2 * ((1-4*x)/(1+4*x))^(1/4).
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MATHEMATICA
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CoefficientList[Series[x/((1-4*x)^(7/4)*(1+4*x)^(1/4)), {x, 0, 40}], x] (* G. C. Greubel, Jun 07 2023 *)
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PROG
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(Magma) [n le 2 select n-1 else 2*(3*Self(n-1) + 8*(n-2)*Self(n-2))/(n-2): n in [1..40]]; // G. C. Greubel, Jun 07 2023
(SageMath)
@CachedFunction
if n<2: return n
else: return 2*(3*a(n-1) + 8*(n-1)*a(n-2))//(n-1)
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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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