%I A085734
%S A085734 1,2,3,16,30,15,272,588,420,105,7936,18960,16380,6300,945,353792,911328,
%T A085734 893640,429660,103950,10395,22368256,61152000,65825760,36636600,
%U A085734 11351340,1891890,135135,1903757312,5464904448,6327135360,3918554640
%N A085734 Triangle read by rows: T(0,0) = 1, T(n,k) = sum(j=max(0,1-k) to n-k, 
               (2^j)*(C(k+j,1+j) + C(k+j+1,1+j))*T(n-1,k-1+j)).
%C A085734 A triangle related to Euler numbers and tangent numbers.
%C A085734 T(n,k) = number of down-up permutations on [2n+2] with k+1 left-to-right 
               maxima. For example, T(1,1) counts the following 3 down-up permutations 
               on [4] each with 2 left-to-right maxima: 2143, 3142, 3241. - David 
               Callan (callan(AT)stat.wisc.edu), Oct 25 2004
%D A085734 Ghislain R. Franssens, On a Number Pyramid Related to the Binomial, Deleham, 
               Eulerian, MacMahon and Stirling number triangles, Journal of Integer 
               Sequences, Vol. 9 (2006), Article 06.4.1.
%F A085734 T(n, k) = A083061(n, k)*2^(n-k) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), 
               Feb 27 2005
%F A085734 E.g.f.: sec(x)^y. - Vladeta Jovovic (vladeta(AT)eunet.rs), May 20 2007
%e A085734 {1}; {2, 3}; {16, 30, 15}; {272, 588, 420, 105}
%Y A085734 T(n, 0) = A000182(n), tangent numbers, T(n, n) = A001147(n+1), sum(k>
               =0, T(n, k) = A000364(n+1), Euler numbers.
%Y A085734 Cf. A088874.
%Y A085734 Sequence in context: A074182 A074759 A102882 this_sequence A034382 A034383 
               A072684
%Y A085734 Adjacent sequences: A085731 A085732 A085733 this_sequence A085735 A085736 
               A085737
%K A085734 nonn,tabl,easy
%O A085734 0,2
%A A085734 Deleham Philippe (kolotoko(AT)wanadoo.fr), Jul 20 2003
%E A085734 Edited and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net) Nov 
               23 2003