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A052861
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E.g.f.: log((1-x)/(1-2*x))*x/(1-x).
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2
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0, 0, 2, 15, 116, 1030, 10644, 127428, 1750944, 27325296, 479288160, 9355658400, 201405744000, 4743245520000, 121334466758400, 3350276227872000, 99309556729958400, 3145135939426252800
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OFFSET
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0,3
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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.: -log((-1+x)/(-1+2*x))*x/(-1+x).
Recurrence: {a(1)=0, a(0)=0, a(2)=2, (-2*n^4-12*n^3-22*n^2-12*n)*a(n)+(5*n^3+28*n^2+45*n+18)*a(n+1)+(-17*n-15-4*n^2)*a(n+2)+(n+2)*a(n+3)}.
a(n) ~ (n-1)! * 2^n * (1 + 2/n + 6/n^2 + 26/n^3 + 150/n^4 + 1082/n^5 + 9366/n^6 + 94586/n^7), coefficients are A000629. - Vaclav Kotesovec, Mar 17 2015
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MAPLE
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spec := [S, {B=Sequence(Z, 1 <= card), C=Cycle(B), S=Prod(B, C)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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CoefficientList[Series[Log[(1-x)/(1-2*x)]*x/(1-x), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)
Flatten[{0, Table[FullSimplify[-n!*(EulerGamma + I*Pi + 2^n*LerchPhi[2, 1, n] + PolyGamma[0, n])], {n, 1, 20}]}] (* Vaclav Kotesovec, Oct 01 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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