##### European J. Combin. 42 (2014), 243--260.

# Dominique Foata, Guo-Niu Han

#
SEIDEL TRIANGLE SEQUENCES AND BI-ENTRINGER NUMBERS

**Abstract.**
This Seidel Triangle Sequence Calculus makes it possible to derive several three-variate generating functions, in particular for the bi-Entringer numbers, which count the alternating permutations according to their lengths, first and last letters. The paper has been motivated by this suprising observation that the number of alternating permutations, whose first letter is greater than its last letter is equal to the Poupard number.

foata at unistra dot fr,
guoniu dot han at unistra dot fr

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