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Fast computation of multinomial coefficients


In a previous publication, we have used the discrete Fourier transform to compute the binomial coefficients. In the present paper, we extend the previously proposed method to compute the multinomial coefficients, analyse its precision and performance. The other methods, analysed in our previous publication, are also extended to the multinomial case. The FFT method presents the best performance to compute all multinomial coefficients at a given level.

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Correspondence to Leonardo C. Araujo.

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Araujo, L.C., Sansão, J.P.H. & Vale-Cardoso, A.S. Fast computation of multinomial coefficients. Numer Algor 88, 837–851 (2021).

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  • Multinomial coefficient
  • Discrete Fourier transform
  • FFT
  • Numerical analysis