This site is supported by donations to The OEIS Foundation. 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 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)^(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 Andrew Howroyd, Table of n, a(n) for n = 0..200 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 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

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

Last modified September 18 02:20 EDT 2019. Contains 327149 sequences. (Running on oeis4.)