public static double SumOfPowers(uint index, int power)
{
double c = (double)1 / (power + 1);
double sum = 0;
for (int i = 0; i <= power; i++)
{
sum += MathTools.NcR(power + 1, i) * MathTools.BrenoulliNumber((uint)i, true) * Math.Pow(index, power + 1 - i);
}
return(Math.Round(sum * c));
}