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A052777
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E.g.f.: x^2*(exp(x)-1)^3.
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1
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0, 0, 0, 0, 0, 120, 1080, 6300, 30240, 130032, 521640, 1996500, 7389360, 26676936, 94486392, 329647500, 1136116800, 3876164832, 13112135496, 44031456900, 146920942800, 487489214520, 1609441068312, 5289755245500, 17315399138400, 56470807803600, 183546483143400
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OFFSET
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0,6
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COMMENTS
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Previous name was: A simple grammar.
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LINKS
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FORMULA
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E.g.f.: x^2*exp(x)^3-3*x^2*exp(x)^2+3*exp(x)*x^2-x^2.
Recurrence: {a(1)=0, a(2)=0, a(4)=0, a(3)=0, (-36*n^2-66*n-6*n^3-36)*a(n)+(11*n+11*n^3+44*n^2-66)*a(n+1)+(-12*n^2+18*n-6*n^3)*a(n+2)+(n^3-n)*a(n+3), a(5)=120}.
For n>2, a(n) = n*(n-1)*(3^(n-2) - 3*2^(n-2) + 3). - Vaclav Kotesovec, Oct 01 2013
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MAPLE
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spec := [S, {B=Set(Z, 1 <= card), S=Prod(Z, Z, B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20); # end of program
seq(6*(n^2-n)*combinat[stirling2](n-2, 3), n=0..20); # Mark van Hoeij, May 29 2013
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MATHEMATICA
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CoefficientList[Series[x^2*(E^x-1)^3, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)
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PROG
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(PARI) x='x+O('x^66); concat([0, 0, 0, 0, 0], Vec( serlaplace( x^2*exp(x)^3-3*x^2*exp(x)^2+3*exp(x)*x^2-x^2))) \\ Joerg Arndt, May 29 2013
(PARI) a(n)={if(n>=2, 3!*n*(n-1)*stirling(n-2, 3, 2), 0)} \\ Andrew Howroyd, Aug 08 2020
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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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