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A342314
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T(n, k) = [x^k] 2^n*(Euler(n, x/2) + Euler(n, x)), where Euler(n, x) are the Euler polynomials. Triangle read by rows, T(n, k) for 0 <= k <= n.
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0
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2, -2, 3, 0, -6, 5, 4, 0, -15, 9, 0, 24, 0, -36, 17, -32, 0, 100, 0, -85, 33, 0, -288, 0, 360, 0, -198, 65, 544, 0, -1680, 0, 1190, 0, -455, 129, 0, 6528, 0, -8064, 0, 3696, 0, -1032, 257, -15872, 0, 48960, 0, -34272, 0, 10920, 0, -2313, 513, 0, -238080, 0, 293760, 0, -133056, 0, 30960, 0, -5130, 1025
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OFFSET
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0,1
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LINKS
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EXAMPLE
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Table starts:
[0] 2
[1] -2, 3
[2] 0, -6, 5
[3] 4, 0, -15, 9
[4] 0, 24, 0, -36, 17
[5] -32, 0, 100, 0, -85, 33
[6] 0, -288, 0, 360, 0, -198, 65
[7] 544, 0, -1680, 0, 1190, 0, -455, 129
[8] 0, 6528, 0, -8064, 0, 3696, 0, -1032, 257
[9] -15872, 0, 48960, 0, -34272, 0, 10920, 0, -2313, 513
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MAPLE
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CoeffList := p -> op(PolynomialTools:-CoefficientList(p, x)):
E := (n, x) -> 2^n*(euler(n, x/2) + euler(n, x));
seq(CoeffList(E(n, x)), n=0..9);
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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