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A052860 A simple grammar: rooted sequences of cycles. 3
0, 1, 2, 9, 56, 440, 4164, 46046, 582336, 8288136, 131090880, 2280970032, 43298796672, 890441326320, 19720847692896, 467964024901200, 11844861486802944, 318549937907204352, 9070876711252816128, 272648086802525651328, 8626452694650322744320 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 5 22:11 EDT 2020. Contains 336214 sequences. (Running on oeis4.)