The boustrophedon ("ox-plowing") transform b of a sequence a is given by b_n | = | sum_(k = 0)^n(n k) a_k E_(n - k) a_n | = | sum_(k = 0)^n (-1)^(n - k)(n k) b_k E_(n - k) for n>=0, where E_n is a secant number or tangent number defined by sum_(n = 0)^∞ E_n x^n/(n!) = sec x + tan x. The exponential generating functions of a and b are related by ℬ(x) = (sec x + tan x) A(x), where the exponential generating function is defined by A(x) = sum_(n = 0)^∞ A_n x^n/(n!).

alternating permutation | Entringer number | secant number | Seidel-Entringer-Arnold triangle | tangent number