A166317 Exponential Riordan array [sec(2x), arctanh(tan(x))].
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
Offset: 0
Examples
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.)
Crossrefs
Programs
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Mathematica
(* The function BellMatrix is defined in A264428. *) rows = 12; M = BellMatrix[Abs[2^#*EulerE[#]]&, rows]; Table[M[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jul 11 2019 *)
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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
Comments