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A052748
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Expansion of e.g.f.: -(log(1-x))^3.
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3
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0, 0, 0, 6, 36, 210, 1350, 9744, 78792, 708744, 7036200, 76521456, 905507856, 11589357312, 159580302336, 2352940786944, 36994905688320, 617953469022720, 10929614667747840, 204073497562936320, 4011658382046919680, 82822558521844224000, 1791791417179298304000
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OFFSET
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0,4
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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.: log(1/(1-x))^3.
Recurrence: {a(1)=0, a(0)=0, a(2)=0, a(3)=6, (-1 - 3*n - 3*n^2 - n^3)*a(n+1) + (9*n + 7 + 3*n^2)*a(n+2) + (-6 - 3*n)*a(n+3) + a(n+4)}.
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MAPLE
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spec := [S, {B=Cycle(Z), S=Prod(B, B, B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
with(combinat):seq(stirling1(j, 3)*3!*(-1)^(j+1), j=0..50); # Leonid Bedratyuk, Aug 07 2012
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PROG
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(PARI) a(n) = {3!*stirling(n, 3, 1)*(-1)^(n+1)} \\ Andrew Howroyd, Jul 27 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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Name changed and terms a(20) and beyond from Andrew Howroyd, Jul 27 2020
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STATUS
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approved
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