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
Examples
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
Programs
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Maple
# The function BellMatrix is defined in A264428. BellMatrix(n -> abs(euler(n)), 10); # Peter Luschny, Jan 29 2016
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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 *)
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]
Extensions
More terms from Jean-François Alcover, Jun 28 2018
Comments