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A179540
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a(0)=0, a(1)=1, a(n)=2*n*(a(n-1)+a(n-2)), n>1.
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1
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0, 1, 4, 30, 272, 3020, 39504, 595336, 10157440, 193549968, 4074148160, 93889358816, 2351124167424, 63570351682240, 1845801323790592, 57281150264184960, 1892062450815217664, 66277682436699689216, 2454110815950536647680, 95774762938714980802048
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OFFSET
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0,3
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LINKS
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FORMULA
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G.f.: (1/G(0)-1)/x/2 where G(k)= 1 - 4*x*k - x^2*(2*k+1)*(2*k+2)/G(k+1); (continued fraction, 1-step). - Sergei N. Gladkovskii, Jul 10 2012
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EXAMPLE
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a(2)=4*(0+1)=4, a(3)=6*(4+1)=30, a(4)=8*(30+4)=272...
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MATHEMATICA
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RecurrenceTable[{a[0]==0, a[1]==1, a[n]==2n(a[n-1]+a[n-2])}, a[n], {n, 30}] (* Harvey P. Dale, Jun 01 2012 *)
CoefficientList[Series[x*E^(-x)/(1-2*x)^(3/2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Feb 23 2014 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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