A238683 Reduced numerators of integral of the Stirling numbers of first kind.
1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -3, 11, -3, 1, 0, 12, -50, 35, -2, 1, 0, -60, 274, -225, 17, -5, 1, 0, 360, -588, 406, -147, 175, -3, 1, 0, -2520, 4356, -3283, 6769, -980, 46, -7, 1, 0, 20160, -36528, 29531, -67284, 7483, -648, 273, -4, 1, 0
Offset: 0
Examples
Fractions: 1, 0, 1/2, 0, -1/2, 1/3, 0, 1, -1, 1/4, 0, -3, 11/3, -3/2, 1/5, etc. numerators: 1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -3, 11, -3, 1, etc.
Programs
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Mathematica
Table[StirlingS1[n, k]/(k+1) // Numerator, {n, 0, 11}, {k, 0, n}] // Flatten
Comments