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A052804
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A simple grammar: cycles of rooted cycles.
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4
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0, 0, 2, 3, 20, 90, 714, 5460, 54704, 580608, 7214040, 96932880, 1452396912, 23507621280, 414102201408, 7827185489760, 158757800613120, 3429996441661440, 78775916315263488, 1914627403408320000, 49126748261368331520, 1326584986873331189760
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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.: log(-1/(-1+log(-1/(-1+x))*x)).
a(n) ~ (n-1)! * r^n, where r = 1.349976485401125... is the root of the equation (r-1)*exp(r) = r. - Vaclav Kotesovec, Oct 01 2013
a(n) = n! * Sum_{k=1..floor(n/2)}(k-1)! * |Stirling1(n-k,k)|/(n-k)!. - Seiichi Manyama, Dec 13 2023
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MAPLE
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spec := [S, {B=Prod(C, Z), C=Cycle(Z), S=Cycle(B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
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MATHEMATICA
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nn = 25; Range[0, nn]! CoefficientList[Series[Log[-1/(-1 + Log[-1/(-1 + x)]*x)], {x, 0, nn}], x] (* T. D. Noe, Feb 21 2013 *)
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PROG
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(PARI)
N = 66; x = 'x + O('x^N);
egf = -log(1 + x*log(1-x)) + 'c0;
gf = serlaplace(egf);
v = Vec(gf); v[1]-='c0; v
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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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