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A134242 Numerators of certain constants c_n = A180609(n)/n! related to Hurwitz numbers. 2
1, -1, 1, -2, 11, -3, -11, 29, 493, -2711, -12406, 2636317, -10597579, -439018457, 1165403153, 118734633647, -105428488301, -4070802683898, 1695077946695371, 56532812889378221, -252968859037883917, -425882179787933647571, 123624959518930226565553, 32729394708071881944913, -5814212300444136523052695 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

Manetti-Ricciardi refer to the c_n as Koszul numbers.

LINKS

Table of n, a(n) for n=1..25.

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

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

D. 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[Numerator[K[n]], {n, 1, 25}] (* Jean-Fran├žois Alcover, Jul 26 2018 *)

CROSSREFS

Cf. A134243, A180609.

Sequence in context: A077805 A104662 A121713 * A087712 A180702 A263328

Adjacent sequences:  A134239 A134240 A134241 * A134243 A134244 A134245

KEYWORD

sign,frac,easy

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 February 28 00:58 EST 2020. Contains 332319 sequences. (Running on oeis4.)