synchcola | May. 28th, 2007

the formula for the first layer is maybe

$c_1 = {d+3 \choose j} \bigg({d-j \over 2} + 1\bigg)\big[d-j \text{ even}\big]$

the formula for the second layer is maybe ("&delta" is d - j)

$\begin{gather*}c_2 = {d + 4 \choose j} 2^{d-j} {(3+\delta)j + (2 + \frac12 \delta)(5 + 2\delta)\over 4(d+3)}\delta\\ \text{(or }0\text{ if }d \text{ is less than }j+2\text{ or }d-j\text{ is not even.})\end{gather*}$

the polynomials that appear in the recurrence are obtained from this by going

$\sum_{j=0}^{d-2l} c_l(d, j) (x-l)^j$

where "l" is the layer.

S	M	T	W	T	F	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30	31

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May. 28th, 2007

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