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A166317
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Exponential Riordan array [sec(2x), arctanh(tan(x))].
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1
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1, 0, 1, 4, 0, 1, 0, 16, 0, 1, 80, 0, 40, 0, 1, 0, 640, 0, 80, 0, 1, 3904, 0, 2800, 0, 140, 0, 1, 0, 49152, 0, 8960, 0, 224, 0, 1, 354560, 0, 319744, 0, 23520, 0, 336, 0, 1, 0, 6225920, 0, 1454080, 0, 53760, 0, 480, 0, 1, 51733504, 0, 54897920, 0, 5230720, 0, 110880, 0, 660, 0, 1
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OFFSET
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0,4
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COMMENTS
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The Bell transform of abs(2^n*euler_number(n)). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 18 2016
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LINKS
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EXAMPLE
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Triangle begins
1;
0, 1;
4, 0, 1;
0, 16, 0, 1;
80, 0, 40, 0, 1;
0, 640, 0, 80, 0, 1;
3904, 0, 2800, 0, 140, 0, 1;
0, 49152, 0, 8960, 0, 224, 0, 1;
354560, 0, 319744, 0, 23520, 0, 336, 0, 1;
0, 6225920, 0, 1454080, 0, 53760, 0, 480, 0, 1;
51733504, 0, 54897920, 0, 5230720, 0, 110880, 0, 660, 0, 1;
Production matrix is
0, 1;
4, 0, 1;
0, 12, 0, 1;
16, 0, 24, 0, 1;
0, 80, 0, 40, 0, 1;
64, 0, 240, 0, 60, 0, 1;
0, 448, 0, 560, 0, 84, 0, 1;
256, 0, 1792, 0, 1120, 0, 112, 0, 1;
0, 2304, 0, 5376, 0, 2016, 0, 144, 0, 1;
which is the exponential Riordan array [cosh(2x),x] minus its top row. (Cf. also A117435.)
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MATHEMATICA
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(* The function BellMatrix is defined in A264428. *)
rows = 12;
M = BellMatrix[Abs[2^#*EulerE[#]]&, rows];
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PROG
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(Sage) # uses[bell_matrix from A264428]
# Adds a column 1, 0, 0, 0, ... at the left side of the triangle.
bell_matrix(lambda n: abs(2^n*euler_number(n)), 10) # Peter Luschny, Jan 18 2016
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CROSSREFS
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Inverse is A166318 which is a signed version of this sequence.
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KEYWORD
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AUTHOR
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STATUS
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approved
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