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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

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

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Last modified November 16 17:39 EST 2018. Contains 317275 sequences. (Running on oeis4.)