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A052771
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E.g.f.: x^3*exp(x)^2.
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3
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0, 0, 0, 6, 48, 240, 960, 3360, 10752, 32256, 92160, 253440, 675840, 1757184, 4472832, 11182080, 27525120, 66846720, 160432128, 381026304, 896532480, 2091909120, 4844421120, 11142168576, 25467813888, 57881395200, 130862284800, 294440140800, 659545915392
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OFFSET
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0,4
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COMMENTS
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The old definition of this sequence was "A simple grammar".
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LINKS
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FORMULA
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Recurrence: {a(1)=0, a(2)=0, a(3)=6, (-2*n-2)*a(n)+(-2+n)*a(n+1)}.
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Chai Wah Wu, May 25 2016
Sum_{n>=3} 1/a(n) = log(2) - 1/2.
Sum_{n>=3} (-1)^(n+1)/a(n) = 9*log(3/2) - 7/2. (End)
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MAPLE
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spec := [S, {B=Set(Z), S=Prod(Z, Z, Z, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Range[0, 30]! CoefficientList[Series[Exp[x]^2 x^3, {x, 0, 30}], x] (* Vincenzo Librandi, Dec 06 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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