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

0,3

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

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

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 *)

Prog

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

Crossrefs

Cf. A007840.

Sequence in context: A276370 A292809 A158883 * A318289 A052840 A308380

Adjacent sequences: A052857 A052858 A052859 * A052861 A052862 A052863

Keyword

easy,nonn

Author

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

Status

approved