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A058928 Denominators of series related to triangular cacti. 1
1, 2, 8, 48, 128, 3840, 46080, 14336, 10321920, 185794560, 6553600, 81749606400 (list; graph; refs; listen; history; text; internal format)
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=0,1,..., ((2*n+1)^(n-1)/(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)^(n-1)), then a(n)=A000165(n)/d_n, with the next few terms, for n=12,...,20, being:

{78479622144, 209924915200, 1428329123020800, 42849873690624000, 170993385472000, 7611536747003904, 1678343852714360832000, 747740921331712000, 2551082656125828464640000}. (End)

REFERENCES

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

LINKS

Table of n, a(n) for n=0..11.

CROSSREFS

Cf. A000165, A052750, A058927.

Sequence in context: A078558 A003032 A193944 * A228288 A173841 A004141

Adjacent sequences:  A058925 A058926 A058927 * A058929 A058930 A058931

KEYWORD

nonn,frac,easy,more

AUTHOR

N. J. A. Sloane, Jan 12 2001

EXTENSIONS

More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Sep 25 2010

STATUS

approved

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Last modified March 26 10:42 EDT 2017. Contains 284111 sequences.