A052804 A simple grammar: cycles of rooted cycles.

0, 0, 2, 3, 20, 90, 714, 5460, 54704, 580608, 7214040, 96932880, 1452396912, 23507621280, 414102201408, 7827185489760, 158757800613120, 3429996441661440, 78775916315263488, 1914627403408320000, 49126748261368331520, 1326584986873331189760

Offset

0,3

Links

Table of n, a(n) for n=0..21.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 765

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

a(0) = a(1) = 0; a(n) = n * (n-2)! + Sum_{k=2..n-1} k * (k-2)! * binomial(n-1,k) * a(n-k). - Seiichi Manyama, Jan 21 2025

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

Cf. A052830, A052858.

Sequence in context: A348311 A066166 A007113 * A267652 A258089 A165960

Adjacent sequences: A052801 A052802 A052803 * A052805 A052806 A052807

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Status

approved