Bkn m+1−k integer n ≥ 1 Thus nX−1 k=0 km = nm+1 m +1 + lower order terms Formulas relating factorial powers and ordinary powers Stirling numbers of xn = X k (n k) xk integer n ≥ 0 the second kind Stirling numbers of xn = X k " n k # xk. If the exponent r is even, then the inequality is valid for all real numbers x.The strict version of the inequality reads. Sum of powers nX−1 k=0 km = 1 m +1 Xm k=0 m +1 k!.
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