Binomial Coefficients

Computes an array of binomial coefficients, with options to balance speed and accuracy.

Purpose

This code is a simple utility that computes binomial coefficients C_{ n , k } for 0 <= n <= n_max and for 0 <= k <= k_max, where n_max and k_max are function inputs, with options to balance speed and accuracy.

Use Case

Its use case is to replace looping through individual calls to Matlab's nchoosek.

Notes

• The file binoms.m is the main function, while the file binoms__demo.mlx demonstrates an example of using the function.
• The user can decide how to balance speed and accuracy of the computation (see the demo for examples).
• Compared to the version '05 Jun 2026', this code should be faster and more accurate when used with any calc_type except 'safe' (in which case this code may be much slower).
• Use of the 'safe' option for the input calc_type may invoke Matlab's Symbolic Math Toolbox, depending on the values of the inputs n_max and k_max.
• Changes to this version were inspired by the comment from the author of [1] on the 'Discussions' section of this project.

References

[1] J. Simon, https://www.mathworks.com/matlabcentral/fileexchange/100174-noverk