A052860 A simple grammar: rooted sequences of cycles.

0, 1, 2, 9, 56, 440, 4164, 46046, 582336, 8288136, 131090880, 2280970032, 43298796672, 890441326320, 19720847692896, 467964024901200, 11844861486802944, 318549937907204352, 9070876711252816128, 272648086802525651328, 8626452694650322744320

Offset: 0

Author

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

Keywords

• easy
• nonn

Comments

Note that here the root is not allowed to be part of the sequence of cycles. We select a root and then form sequences from the cycles in the permutations of the remaining n-1 elements. Cf. A218817. - Geoffrey Critzer, Nov 06 2012

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..150
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 828

Crossrefs

Cf. A007840.

Programs

Maple

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

Mathematica

nn=20;a=Log[1/(1-x)];Range[0,nn]!CoefficientList[Series[x/(1-a) ,{x,0,nn}],x]  (* Geoffrey Critzer, Nov 06 2012 *)

PARI

a(n)=n!*polcoeff(x/(1+log(1-x +x*O(x^n))),n) \\ Paul D. Hanna, Jul 19 2006

Formula

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

a(n) = n*A007840(n-1). a(n) = n!*Sum_{k=0..n-1} a(k)/k!/(n-k) for n>=1 with a(0)=0. - Paul D. Hanna, Jul 19 2006

a(n) ~ n! * exp(n-1) / (exp(1)-1)^n. - Vaclav Kotesovec, Mar 16 2014