## Why Delannoy numbers?(English)Zbl 1074.01012

Summary: This article is not a research paper, but a little note on the history of combinatorics: we present here a tentative short biography of Henri Delannoy, and a survey of his most notable works. This answers the question raised in the title, as these works are related to lattice paths enumeration, to the so-called Delannoy numbers, and were the first general way to solve Ballot-like problems.

### MSC:

 01A70 Biographies, obituaries, personalia, bibliographies 60G50 Sums of independent random variables; random walks 05A15 Exact enumeration problems, generating functions 05A10 Factorials, binomial coefficients, combinatorial functions 82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics

### Keywords:

lattice paths enumeration; ballot problems
Full Text:

### Online Encyclopedia of Integer Sequences:

Square array of Delannoy numbers D(i,j) (i >= 0, j >= 0) read by antidiagonals.
a(n) = n*2^n.

### References:

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