

A058928


Denominators of series related to triangular cacti.


2



1, 2, 8, 48, 128, 3840, 46080, 14336, 10321920, 185794560, 6553600, 81749606400, 78479622144, 209924915200, 1428329123020800, 42849873690624000, 170993385472000, 7611536747003904, 1678343852714360832000, 747740921331712000, 2551082656125828464640000
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OFFSET

0,2


COMMENTS

Contribution by L. Edson Jeffery, Jan 09 2012 (Start):
The reference [Bergeron, et al.] lists the first few terms of the relevant series as S(x) = x + (1/2)*x^3 + (5/8)*x^5 + (49/48)*x^7 + (243/128)*x^9 + ..., from which the denominators were taken for this sequence and the numerators for A058927. This leads to the following
Conjecture: S(x) = Sum_{n>=0} ((2*n+1)^(n1)/(n!*2^n))*x^(2*n+1) = (A052750(n)/A000165(n))*x^(2*n+1). Letting D_n be the set of divisors of n! and d_n = max(k in D_n : k  (2*n+1)^(n1)), then a(n)=A000165(n)/d_n. (End)
The above conjecture is correct and follows from formula given in A034940 for the number of rooted labeled triangular cacti with 2n+1 nodes.  Andrew Howroyd, Aug 30 2018


REFERENCES

F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and TreeLike Structures, Camb. 1998, p. 307.


LINKS

Andrew Howroyd, Table of n, a(n) for n = 0..200


FORMULA

a(n) = denominator(A034940(n)/(2*n+1)!) = denominator((2*n+1)^(n1)/(2^n*n!)).  Andrew Howroyd, Aug 30 2018


PROG

(PARI) a(n)={denominator((2*n+1)^(n1)/(2^n*n!))} \\ Andrew Howroyd, Aug 30 2018


CROSSREFS

Cf. A000165, A034940, A052750, A058927.
Sequence in context: A078558 A003032 A193944 * A228288 A292277 A173841
Adjacent sequences: A058925 A058926 A058927 * A058929 A058930 A058931


KEYWORD

nonn,frac,easy


AUTHOR

N. J. A. Sloane, Jan 12 2001


EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010
Terms a(12) and beyond from Andrew Howroyd, Aug 30 2018


STATUS

approved



