A147312 Riordan array [1,log(sec(x)+tan(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 A000111. Inverse is A147311.

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

The product [sec(x),x]*A147312 is A147309.

Apart from signs, same as A147311. - N. J. A. Sloane, Nov 07 2008

Also the Bell transform of the absolute 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.

Formula

T(n,m)=sum(k=m..n, A147315(n,k)*stirling1(k,m)), n>0,k>0, T(0,0)=1, T(0,k)=0, k>0. [From Vladimir Kruchinin, Mar 10 2011]

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 -> abs(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[Abs[EulerE[#]] &, rows];
Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *)

Crossrefs

Sequence in context: A272774 A333274 A147311 * A352771 A271423 A372762

Adjacent sequences: A147309 A147310 A147311 * A147313 A147314 A147315

Keyword

easy,nonn,tabl

Author

Paul Barry, Nov 05 2008

Extensions

More terms from Jean-François Alcover, Jun 28 2018

Status

approved