Problem 46034. Construct the Seidel-Entringer-Arnold triangle
Several problems in Cody ask us to construct part or all of triangles in which entries follow a pattern. Cody Problems 37, 1463, 44037, and 44904 involve Pascal's triangle, which consists of the binomial coefficients, and Cody Problem 1845 extends Pascal's triangle to a pyramid. Cody Problem 45460 involves the Bernoulli triangle, which consists of partial sums of the binomial coefficients.
This problem deals with the Seidel-Entringer-Arnold triangle (also called the Euler-Bernoulli triangle and the secant-tangent triangle). The first eight layers are
The name "secant-tangent triangle" arises because the sides contain the coefficients in the Taylor series for and :
Construct the nth layer of this triangle.
Hint: Use the boustrophedon (or ox-plowing) rule.
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