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A052804 A simple grammar: cycles of rooted cycles. 4
0, 0, 2, 3, 20, 90, 714, 5460, 54704, 580608, 7214040, 96932880, 1452396912, 23507621280, 414102201408, 7827185489760, 158757800613120, 3429996441661440, 78775916315263488, 1914627403408320000, 49126748261368331520, 1326584986873331189760 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
FORMULA
E.g.f.: log(-1/(-1+log(-1/(-1+x))*x)).
E.g.f.: -log(1 + x*log(1-x)). - Arkadiusz Wesolowski, Feb 21 2013
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
MAPLE
spec := [S, {B=Prod(C, Z), C=Cycle(Z), S=Cycle(B)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);
MATHEMATICA
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 *)
PROG
(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
/* Joerg Arndt, Feb 21 2013 */
CROSSREFS
Sequence in context: A348311 A066166 A007113 * A267652 A258089 A165960
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
STATUS
approved

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Last modified March 1 15:29 EST 2024. Contains 370440 sequences. (Running on oeis4.)