A147311 Riordan array [1, arcsin(tanh(x))].

1, 0, 1, 0, 0, 1, 0, -1, 0, 1, 0, 0, -4, 0, 1, 0, 5, 0, -10, 0, 1, 0, 0, 40, 0, -20, 0, 1, 0, -61, 0, 175, 0, -35, 0, 1, 0, 0, -768, 0, 560, 0, -56, 0, 1, 0, 1385, 0, -4996, 0, 1470, 0, -84, 0, 1, 0, 0, 24320, 0, -22720, 0, 3360, 0, -120, 0, 1, 0, -50521, 0, 214445, 0, -81730, 0, 6930, 0, -165, 0, 1

Offset

0,13

Comments

Row sums are A012123. Inverse is A147312.

Production array is [cos(x),x] with a column of 0's prepended.

The product [sech(x),x]*A147311 is A147308.

Apart from signs, same as A147312. - N. J. A. Sloane, Nov 07 2008

Also the Bell transform of the Euler numbers. For the definition of the Bell transform see A264428. - Peter Luschny, Jan 29 2016

Links

Table of n, a(n) for n=0..77.

Example

Triangle begins
  1,
  0,   1,
  0,   0,   1,
  0,  -1,   0,   1,
  0,   0,  -4,   0,   1,
  0,   5,   0, -10,   0,   1,
  0,   0,  40,   0, -20,   0,   1

Maple

# The function BellMatrix is defined in A264428.
BellMatrix(n -> euler(n), 10); # Peter Luschny, Jan 29 2016

Mathematica

BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
rows = 12;
B = BellMatrix[EulerE, rows];
Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 26 2018, after Peter Luschny *)

Crossrefs

Sequence in context: A143784 A272774 A333274 * A147312 A352771 A271423

Adjacent sequences: A147308 A147309 A147310 * A147312 A147313 A147314

Keyword

easy,sign,tabl

Author

Paul Barry, Nov 05 2008

Extensions

More terms from Jean-François Alcover, Jun 26 2018

Status

approved