A134243 Denominators of certain constants c_n = A180609(n)/n! related to Hurwitz numbers.
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
Offset: 1
Examples
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, ...
Links
- 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
Programs
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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-François Alcover, Jul 26 2018 *)
Formula
Manetti-Ricciardi Theorem 4.4 give a recurrence for the c_n in terms of Stirling numbers.
Extensions
More terms from Manetti-Ricciardi added by N. J. A. Sloane, May 25 2016
Comments