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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

Table of n, a(n) for n=0..65.

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-Fran├žois 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.)