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A058927 Numerators of series related to triangular cacti. 1
1, 1, 5, 49, 243, 14641, 371293, 253125, 410338673, 16983563041, 1400846643, 41426511213649 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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 numerators were taken for this sequence and the denominators for A058928. 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)=A052750(n)/d_n, with the next few terms, for n=12,...,20, being:

{95367431640625, 617673396283947, 10260628712958602189, 756943935220796320321, 7474615974418932603, 827909024473876953125, 456487940826035155404146917, 510798409623548623605717, 4394336169668803158610484050361}. (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.

FORMULA

G.f. A(x) satisfies A(x)=exp(x*A(x)^2). [Vladimir Kruchinin, Feb 09 2013]

CROSSREFS

Cf. A000165, A052750, A058928.

Sequence in context: A007406 A196326 A273385 * A083224 A201358 A242035

Adjacent sequences:  A058924 A058925 A058926 * A058928 A058929 A058930

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 June 26 02:24 EDT 2017. Contains 288749 sequences.