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A134242
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Numerators of certain constants c_n = A180609(n)/n! related to Hurwitz numbers.
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2
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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
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OFFSET
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1,4
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COMMENTS
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Manetti-Ricciardi refer to the c_n as Koszul numbers.
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LINKS
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FORMULA
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Manetti-Ricciardi Theorem 4.4 give a recurrence for the c_n in terms of Stirling numbers.
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EXAMPLE
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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, ...
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MATHEMATICA
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K[1] = 1;
K[n_] := K[n] = -2/((n+2)(n-1)) Sum[StirlingS2[n+1, i] K[i], {i, 1, n-1}];
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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