A371687 Triangle read by rows: T(n, k) = (-1)^(n-k) * (2*n + 1)! * [y^(2*k)] [x^(2*n+1)] arctan(sec(x*y)*tanh(x)).
1, 4, 3, 80, 80, 25, 3904, 5376, 2660, 427, 354560, 626688, 433440, 131712, 12465, 51733504, 111738880, 99242880, 43804992, 9021540, 555731, 11070525440, 28258074624, 30647302400, 17666508288, 5509286640, 816337808, 35135945
Offset: 0
Examples
Triangle starts: [0] 1; [1] 4, 3; [2] 80, 80, 25; [3] 3904, 5376, 2660, 427; [4] 354560, 626688, 433440, 131712, 12465; [5] 51733504, 111738880, 99242880, 43804992, 9021540, 555731;
Crossrefs
Programs
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Maple
egf := arctan(sec(x*y)*tanh(x)): serx := simplify(series(egf, x, 26)): coeffx := n -> n!*coeff(serx, x, n): seq(print(seq((-1)^(n-k)*coeff(coeffx(2*n+1), y, 2*k), k = 0..n)), n = 0..6);
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