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

Author

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

Keywords

• easy
• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..419
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 771

Crossrefs

Cf. A003713, A185393.

Programs

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 *)

PARI

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

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