Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
Euler's partition theorem and the combinatorics of -sequences
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“Pascal-like” triangle for <strong>the</strong> l-nomial coefficient:<br />
1<br />
1 1<br />
1 3 1<br />
1 8 8 1<br />
1 21 56 21 1<br />
1 55 385 385 55 1<br />
1 144 2640 6930 2640 144 1<br />
Theorem<br />
( ) n (l) ( )<br />
= (a (l) n − 1 (l) (<br />
k<br />
k+1 − a(l) k ) + (a (l)<br />
n − 1<br />
k<br />
n−k − a(l) n−k−1 ) k − 1<br />
) (l)
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