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A052727
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A simple context-free grammar in a labeled universe.
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1
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0, 1, 4, 24, 288, 4800, 103680, 2741760, 85800960, 3100446720, 127037030400, 5819550105600, 294727768473600, 16350861400473600, 986127353590579200, 64238655955009536000, 4495021381191204864000, 336249161369543245824000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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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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E.g.f.: 1/2-1/2*(1-4*x-4*x^2)^(1/2)
Recurrence: {a(1)=1, a(2)=4, (-4*n^2+4)*a(n) +(-4*n-2)*a(n+1) +a(n+2) =0.
a(n) ~ sqrt(2-sqrt(2))* ((1+sqrt(2))/exp(1))^n * (2*n)^(n-1). - Vaclav Kotesovec, Sep 30 2013
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MAPLE
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spec := [S, {B=Prod(S, S), S=Union(B, Z, C), C=Prod(Z, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[1/2-1/2*(1-4*x-4*x^2)^(1/2), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 30 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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STATUS
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approved
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