A052809 A simple grammar: number of cycles of cycles.

0, 0, 2, 6, 28, 175, 1368, 12838, 140656, 1762794, 24878320, 390495336, 6748280064, 127324033824, 2604355096224, 57404425654080, 1356401049662208, 34202807058719568, 916723959720053760

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..419

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 771

Formula

E.g.f.: log(-1/(-1+log(-1/(-1+x))))*x.

E.g.f.: -log(1+log(1-x))*x. - Vaclav Kotesovec, Oct 01 2013

a(n) ~ (n-1)! * (exp(1)/(exp(1)-1))^(n-1). - Vaclav Kotesovec, Oct 01 2013

a(n) = n * Sum_{k=1..n-1} (k-1)! * |Stirling1(n-1,k)| = n * A003713(n-1). - Seiichi Manyama, May 20 2022

Maple

spec := [S, {B=Cycle(C), C=Cycle(Z), S=Prod(B, Z)}, labeled]: seq(combstruct[count](spec, size=n), n=0..20);

Mathematica

CoefficientList[Series[-Log[1+Log[1-x]]*x, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Oct 01 2013 *)

Prog

(PARI) a(n) = n*sum(k=1, n-1, (k-1)!*abs(stirling(n-1, k, 1))); \\ Seiichi Manyama, May 20 2022

Crossrefs

Cf. A003713, A185393.

Sequence in context: A207386 A088501 A140092 * A136631 A002435 A276911

Adjacent sequences: A052806 A052807 A052808 * A052810 A052811 A052812

Keyword

easy,nonn

Author

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

Status

approved