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Riordan array [1,log(sec(x)+tan(x))].
2

%I #15 Jun 28 2018 02:43:02

%S 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,

%T 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,

%U 0,24320,0,22720,0,3360,0,120,0,1,0,50521,0,214445,0,81730,0,6930,0,165,0,1

%N Riordan array [1,log(sec(x)+tan(x))].

%C Row sums are A000111. Inverse is A147311.

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

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

%C Apart from signs, same as A147311. - _N. J. A. Sloane_, Nov 07 2008

%C Also the Bell transform of the absolute Euler numbers. For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 29 2016

%F 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]

%e Triangle begins

%e 1,

%e 0, 1,

%e 0, 0, 1,

%e 0, 1, 0, 1,

%e 0, 0, 4, 0, 1,

%e 0, 5, 0, 10, 0, 1,

%e 0, 0, 40, 0, 20, 0, 1

%p # The function BellMatrix is defined in A264428.

%p BellMatrix(n -> abs(euler(n)), 10); # _Peter Luschny_, Jan 29 2016

%t BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

%t rows = 12;

%t B = BellMatrix[Abs[EulerE[#]] &, rows];

%t Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 28 2018, after _Peter Luschny_ *)

%K easy,nonn,tabl

%O 0,13

%A _Paul Barry_, Nov 05 2008

%E More terms from _Jean-François Alcover_, Jun 28 2018