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

1,2

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-François Alcover, Jul 26 2018 *)

Crossrefs

Cf. A134242, A180609.

Sequence in context: A075095 A178343 A156136 * A182779 A199673 A335942

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