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A134243 Denominators of certain constants c_n = A180609(n)/n! related to Hurwitz numbers. 2
1, 2, 2, 3, 12, 4, 6, 4, 12, 6, 15, 60, 120, 60, 20, 60, 3, 5, 60, 120, 8, 1260, 2520, 168, 56, 168, 168, 840, 84, 840, 21, 140, 420, 630, 120, 280, 420, 840, 504, 2520, 840, 840, 315, 2520, 2520, 315, 84, 90, 30, 180, 360, 120, 120, 210, 24, 495, 1980, 2640, 55440, 315, 55440, 45, 2772, 6930, 27720, 9240, 770, 1848, 27720, 27720 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Manetti-Ricciardi refer to the c_n as Koszul numbers.

LINKS

Table of n, a(n) for n=1..70.

Marco Manetti and Giulia Ricciardi, Universal Lie formulas for higher antibrackets, arXiv preprint arXiv:1509.09032 [math.QA], 2015-2016.

Sergey Shadrin and Dimitri Zvonkine, Changes of variables in ELSV-type formulas, Michigan Mathematical Journal, vol. 55 (2007), 209-228.

Dimitri Zvonkine, Home Page

FORMULA

Manetti-Ricciardi Theorem 4.4 give a recurrence for the c_n in terms of Stirling numbers.

EXAMPLE

The fractions are 1, -1/2, 1/2, -2/3, 11/12, -3/4, -11/6, 29/4, 493/12, -2711/6, -12406/15, 2636317/60, -10597579/120, -439018457/60, 1165403153/20, 118734633647/60, ...

MATHEMATICA

K[1] = 1;

K[n_] := K[n] = -2/((n+2)(n-1)) Sum[StirlingS2[n+1, i] K[i], {i, 1, n-1}];

Table[Denominator[K[n]], {n, 1, 70}] (* Jean-Fran├žois Alcover, Jul 26 2018 *)

CROSSREFS

Cf. A134242, A180609.

Sequence in context: A075095 A178343 A156136 * A182779 A199673 A240133

Adjacent sequences:  A134240 A134241 A134242 * A134244 A134245 A134246

KEYWORD

nonn,frac

AUTHOR

N. J. A. Sloane, Jan 30 2008

EXTENSIONS

More terms from Manetti-Ricciardi added by N. J. A. Sloane, May 25 2016

STATUS

approved

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Last modified September 21 13:37 EDT 2019. Contains 327253 sequences. (Running on oeis4.)