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%I #25 Jul 26 2018 11:31:29
%S 1,-1,1,-2,11,-3,-11,29,493,-2711,-12406,2636317,-10597579,-439018457,
%T 1165403153,118734633647,-105428488301,-4070802683898,
%U 1695077946695371,56532812889378221,-252968859037883917,-425882179787933647571,123624959518930226565553,32729394708071881944913,-5814212300444136523052695
%N Numerators of certain constants c_n = A180609(n)/n! related to Hurwitz numbers.
%C Manetti-Ricciardi refer to the c_n as Koszul numbers.
%H M Manetti, G Ricciardi, <a href="http://arxiv.org/abs/1509.09032">Universal Lie formulas for higher antibrackets</a>, arXiv preprint arXiv:1509.09032 [math.QA], 2015-2016.
%H S. Shadrin and D. Zvonkine, <a href="http://dx.doi.org/10.1307/mmj/1177681994">Changes of variables in ELSV-type formulas</a>, Michigan Mathematical Journal, vol. 55 (2007), 209-228.
%H D. Zvonkine, <a href="http://www.math.jussieu.fr/~zvonkine/">Home Page</a>
%F Manetti-Ricciardi Theorem 4.4 give a recurrence for the c_n in terms of Stirling numbers.
%e 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, ...
%t K[1] = 1;
%t K[n_] := K[n] = -2/((n+2)(n-1)) Sum[StirlingS2[n+1, i] K[i], {i, 1, n-1}];
%t Table[Numerator[K[n]], {n, 1, 25}] (* _Jean-François Alcover_, Jul 26 2018 *)
%Y Cf. A134243, A180609.
%K sign,frac,easy
%O 1,4
%A _N. J. A. Sloane_, Jan 30 2008
%E More terms from Manetti-Ricciardi added by _N. J. A. Sloane_, May 25 2016