Journal of Integer Sequences, Vol. 22 (2019), Article 19.8.3

Digit Sums Generalizing Binomial Coefficients

Ji Young Choi
Department of Mathematics
Shippensburg University of Pennsylvania
1871 Old Main Drive
Shippensburg, PA 17257


We define four different generalizations of binomial coefficients, using the digit sum of a string with digits in {0, 1, 2, ..., g}, for positive integers g. We identify one generalization with the extended binomial coefficients, and we express every other generalization in terms of the extended binomial coefficients. We also express every generalization in terms of the binomial coefficients and find the explicit formula for each generalization.

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(Concerned with sequences A005773 A007318 A008287 A027907 A071976.)

Received July 7 2019; revised version received December 9 2019. Published in Journal of Integer Sequences, December 11 2019.

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