EXTENSION OF EULER NUMBERS AND RECORDS OF UP-DOWN PERMUTATIONS

[摘要] We study the sequence of polynomials C(n)(x, y) defined through the recurrence C0(x, y)=1, C(n)(x, y)=x(y+1)C(n)-1(x+2,y+2)-xyC(n-1)(x,y), which turns out to be an extension of Euler numbers. We give a combinatorial interpretation of these numbers in terms of down-up permutations with respect to the numbers of even and odd upper records and a continued fraction expansion for their ordinary generating function. (C) 1994 Academic Press, Inc.

[发布日期] 1994-10-01