%I A033877
%S A033877 1,1,2,1,4,6,1,6,16,22,1,8,30,68,90,1,10,48,146,304,394,1,12,70,264,714,
%T A033877 1412,1806,1,14,96,430,1408,3534,6752,8558,1,16,126,652,2490,7432,17718,
%U A033877 33028,41586,1,18,160,938,4080,14002,39152,89898,164512,206098,1,20,198
%N A033877 Triangular array associated with Schroeder numbers: T(1,* ) = 1; T(n,
               k) = 0 if k<n; T(n,k) = T(n,k-1) + T(n-1,k-1) + T(n-1,k).
%C A033877 The diagonals of this triangle are self-convolutions of the main diagonal 
               A006318 : 1, 2, 6, 22, 90, 394, 1806, . . . - Philippe DELEHAM, May 
               15 2005
%C A033877 A106579 is in some ways a better version of this sequence, but since 
               this was entered first it will be the main entry for this triangle.
%H A033877 T. D. Noe, <a href="b033877.txt">Rows n=1..50 of triangle, flattened</
               a>
%H A033877 H. Bottomley, <a href="a001003.gif">Illustration of initial terms</a>
%H A033877 E. Pergola and R. A. Sulanke, <a href="http://www.cs.uwaterloo.ca/journals/
               JIS/index.html">Schroeder Triangles, Paths and Parallelogram Polyominoes</
               a>, J. Integer Sequences, 1 (1998), #98.1.7.
%H A033877 R. A. Sulanke, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Objects counted by the central Delannoy numbers</a>, J. Integer Seq. 
               6 (2003), Article 03.1.5, 19 pp.
%F A033877 As an upper right triangle: a(n, k) = a(n, k-1)+a(n-1, k-1)+a(n-1, k) 
               if k >= n >= 0 and a(n, k)=0 otherwise.
%F A033877 G.f.: Sum T(n, k)*x^n*y^k = (1-x*y-(x^2*y^2-6*x*y+1)^(1/2)) / (x*(2*y+x*y-1+(x^2*y^2-6*x*y+1)^(1/
               2))). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 16 2003
%F A033877 Another version of A000007 DELTA [0, 2, 1, 2, 1, 2, 1, 2, 1, 2, ...] 
               = 1, 1, 0, 1, 2, 0, 1, 4, 6, 0, 1, 6, 16, 22, 0, 1, ..., where DELTA 
               is Deleham's operator defined in A084938.
%t A033877 T[ 1, _ ] := 1; T[ n_, k_ ]/;(k<n) := 0; T[ n_, k_ ] := T[ n, k ]=T[ 
               n, k-1 ]+T[ n-1, k-1 ]+T[ n-1, k ];
%Y A033877 Essentially same triangle as A080245 but with rows read in reversed order. 
               Also essentially the same triangle as A106579.
%Y A033877 Cf. A008288, A006318, A006319, A006320, A006321, A001003 (row sums), 
               A000007, A084938.
%Y A033877 Cf. A026003 (antidiagonal sums).
%Y A033877 Sequence in context: A063872 A033884 A062344 this_sequence A059369 A098473 
               A121757
%Y A033877 Adjacent sequences: A033874 A033875 A033876 this_sequence A033878 A033879 
               A033880
%K A033877 nonn,tabl,nice
%O A033877 1,3
%A A033877 N. J. A. Sloane (njas(AT)research.att.com).
%E A033877 More terms from David W. Wilson (davidwwilson(AT)comcast.net)