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 A166317 Exponential Riordan array [sec(2x), arctanh(tan(x))]. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The Bell transform of abs(2^n*euler_number(n)). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 18 2016 LINKS EXAMPLE 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.) 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 *) PROG (Sage) # The function bell_matrix is defined in 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 CROSSREFS Row sums are A012259(n+1). Inverse is A166318 which is a signed version of this sequence. Cf. A117435, A264428. Sequence in context: A117436 A136448 A166318 * A068346 A006838 A061309 Adjacent sequences:  A166314 A166315 A166316 * A166318 A166319 A166320 KEYWORD easy,nonn,tabl AUTHOR Paul Barry, Oct 11 2009 STATUS approved

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Last modified December 14 15:08 EST 2019. Contains 329979 sequences. (Running on oeis4.)