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Multinomial Coefficient

The multinomial Coefficients

(x_1, x_2, \ldots)! = {x_1+x_2+\ldots\over x_1! x_2! \cdots}

are the terms in the Multinomial Series expansion. They satisfy
$\displaystyle (x_1, x_2, x_3, \ldots)$ $\textstyle =$ $\displaystyle (x_1+x_2, x_3, \ldots)(x_1, x_2)$  
  $\textstyle =$ $\displaystyle (x_1+x_2+x_3, \ldots)(x_1, x_2, x_3)=\ldots$  

(Beeler et al. 1972, Item 44).

See also Binomial Coefficient, Multinomial Series


Abramowitz, M. and Stegun, C. A. (Eds.). ``Multinomial Coefficients.'' §24.1.2 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 823-824, 1972.

Beeler, M.; Gosper, R. W.; and Schroeppel, R. HAKMEM. Cambridge, MA: MIT Artificial Intelligence Laboratory, Memo AIM-239, Feb. 1972.

Spiegel, M. R. Theory and Problems of Probability and Statistics. New York: McGraw-Hill, p. 113, 1992.

© 1996-9 Eric W. Weisstein