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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) # 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
CROSSREFS
Row sums are A012259(n+1).
Inverse is A166318 which is a signed version of this sequence.
Sequence in context: A117436 A136448 A166318 * A068346 A348304 A006838
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Oct 11 2009
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)