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 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 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 A356346 A292277 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

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Last modified September 26 02:05 EDT 2022. Contains 356986 sequences. (Running on oeis4.)