login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
From 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)^(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. (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 Tree-Like Structures, Camb. 1998, p. 307.
LINKS
FORMULA
a(n) = denominator(A034940(n)/(2*n+1)!) = denominator((2*n+1)^(n-1)/(2^n*n!)). - Andrew Howroyd, Aug 30 2018
PROG
(PARI) a(n)={denominator((2*n+1)^(n-1)/(2^n*n!))} \\ Andrew Howroyd, Aug 30 2018
CROSSREFS
Sequence in context: A078558 A003032 A193944 * A228288 A356346 A292277
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)