= Solution
Set $d=k-1$ and let $e_m(t_{i+1},\ldots,t_{i+d})$ be the <elementary symmetric polynomial> of degree $m$ in the interior knots, with $e_0=1$. Expand the <Marsden identity> in powers of $x$. The coefficient of $x^{d-m}$ on the left is $(-1)^m\binom dm t^m$; that coefficient in $\omega_i(x)$ is $(-1)^me_m(t_{i+1},\ldots,t_{i+d})$. Comparing and cancelling the sign proves \b[the <monomial B-spline coefficients>]:
$$
\boxed{a_i^{(m)}=\frac{e_m(t_{i+1},\ldots,t_{i+k-1})}{\binom{k-1}{m}},\qquad0\leq m\leq k-1.}
$$
For $m=0$ this gives <partition of unity> on the basic interval. For $m=1$ it gives the <Greville abscissae>, the arithmetic means of the $k-1$ interior knots. For the top degree it gives their product. When $k=1$, only $m=0$ occurs and the empty symmetric <polynomial> is one.
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