Journal of Integer Sequences, Vol. 17 (2014), Article 14.10.4

A Note on Extended Binomial Coefficients

Thorsten Neuschel
Department of Mathematics
KU Leuven
Celestijnenlaan 200B
Box 2400
BE-3001 Leuven


We study the distribution of the extended binomial coefficients by deriving a complete asymptotic expansion with uniform error terms. We obtain the expansion from a local central limit theorem and we state all coefficients explicitly as sums of Hermite polynomials and Bernoulli numbers.

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(Concerned with sequences A002426 A005190 A008287 A027907 A035343.)

Received July 29 2014; revised versions received October 1 2014; November 3 2014; November 4 2014. Published in Journal of Integer Sequences, November 4 2014.

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