%I #19 May 02 2015 10:48:36

%S 1,1,1,1,3,2,1,5,10,6,1,7,22,38,22,1,9,38,98,158,90,1,11,58,194,450,

%T 698,394,1,13,82,334,978,2126,3218,1806,1,15,110,526,1838,4942,10286,

%U 15310,8558,1,17,142,778,3142,9922,25150,50746,74614,41586

%N Triangular array associated with Schroeder numbers.

%C Transpose of triangular array A132372. - _Michel Marcus_, May 02 2015

%H E. Pergola and R. A. Sulanke, <a href="https://cs.uwaterloo.ca/journals/JIS/PergolaSulanke/">Schroeder Triangles, Paths and Parallelogram Polyominoes</a>, J. Integer Sequences, 1 (1998), #98.1.7.

%e This triangle reads:

%e 1

%e 1 1

%e 1 3 2

%e 1 5 10 6

%e 1 7 22 38 22

%e 1 9 38 98 158 90

%e 1 11 58 194 450 698 394

%e 1 13 82 334 978 2126 3218 1806

%e 1 15 110 526 1838 4942 10286 15310 558

%e 1 17 142 778 3142 9922 25150 50746 74614 41586

%o (PARI) lgs(n) = if( n<1, 1, sum( k=0, n, 2^k * binomial( n, k) * binomial( n, k-1)) / n) /* A006318 */

%o T(n, k) = if (k>n, 0, if (k==0, 1, if (n==0, 1, if ((n==k), lgs(n-1), T(n,k-1) + T(n-1,k-1) + T(n-1,k)))));

%o tabl(nn) = {for (n=0, nn, for (m=0, n, print1(T(n, m), ", ");); print(););} \\ _Michel Marcus_, May 02 2015

%K nonn,tabl,easy

%O 0,5

%A _N. J. A. Sloane_.

%E Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003