static Frac[] FaulhaberTriangle(int p)
{
Frac[] coeffs = new Frac[p + 1];
for (int i = 0; i < p + 1; i++)
{
coeffs[i] = Frac.ZERO;
}
Frac q = new Frac(1, p + 1);
int sign = -1;
for (int j = 0; j <= p; j++)
{
sign *= -1;
coeffs[p - j] = q * new Frac(sign, 1) * new Frac(Binomial(p + 1, j), 1) * Bernoulli(j);
}
return(coeffs);
}
static Frac Bernoulli(int n)
{
if (n < 0)
{
throw new ArgumentException("n may not be negative or zero");
}
Frac[] a = new Frac[n + 1];
for (int m = 0; m <= n; m++)
{
a[m] = new Frac(1, m + 1);
for (int j = m; j >= 1; j--)
{
a[j - 1] = (a[j - 1] - a[j]) * new Frac(j, 1);
}
}
// returns 'first' Bernoulli number
if (n != 1)
{
return(a[0]);
}
return(-a[0]);
}