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A052760
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Expansion of e.g.f.: x^2*(exp(x)-1)^2.
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3
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0, 0, 0, 0, 24, 120, 420, 1260, 3472, 9072, 22860, 56100, 134904, 319176, 745108, 1719900, 3931680, 8912352, 20053404, 44825940, 99613960, 220200120, 484441188, 1061157900, 2315254704, 5033163600, 10905189100, 23555209860, 50734299672, 108984793512
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OFFSET
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0,5
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COMMENTS
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Original name: a simple grammar.
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LINKS
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FORMULA
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E.g.f.: x^2*exp(x)^2-2*exp(x)*x^2+x^2.
Recurrence: {a(1)=0, a(2)=0, a(3)=0, a(4)=24, (2*n^2+6*n+4)*a(n)+(6-3*n^2-3*n)*a(n+1)+(n^2-n)*a(n+2)}.
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MAPLE
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spec := [S, {B=Set(Z, 1 <= card), S=Prod(B, B, Z, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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Part[#, Range[1, Length[#], 1]]&@(Array[#!&, Length[#], 0] #)&@CoefficientList[Series[x^2 Exp[x]^2 - 2 Exp[x] x^2 + x^2, {x, 0, 30}], x]//ExpandAll (* Vincenzo Librandi, May 05 2013 *)
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PROG
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(Magma) [0, 0, 0] cat [n*(n-1)*(2^n-8)/4: n in [3..30]]; // Vincenzo Librandi, May 05 2013
(PARI) a(n) = if(n<4, 0, n*(n-1)*(2^n-8)/4); \\ Joerg Arndt, May 06 2013
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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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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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