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%I A033878 #19 May 02 2015 10:48:36
%S A033878 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 A033878 698,394,1,13,82,334,978,2126,3218,1806,1,15,110,526,1838,4942,10286,
%U A033878 15310,8558,1,17,142,778,3142,9922,25150,50746,74614,41586
%N A033878 Triangular array associated with Schroeder numbers.
%C A033878 Transpose of triangular array A132372. - _Michel Marcus_, May 02 2015
%H A033878 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 A033878 This triangle reads:
%e A033878 1
%e A033878 1  1
%e A033878 1  3   2
%e A033878 1  5   10   6
%e A033878 1  7   22   38   22
%e A033878 1  9   38   98   158   90
%e A033878 1  11  58   194  450   698   394
%e A033878 1  13  82   334  978   2126  3218   1806
%e A033878 1  15  110  526  1838  4942  10286  15310   558
%e A033878 1  17  142  778  3142  9922  25150  50746  74614  41586
%o A033878 (PARI) lgs(n) = if( n<1, 1, sum( k=0, n, 2^k * binomial( n, k) * binomial( n, k-1)) / n) /* A006318 */
%o A033878 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 A033878 tabl(nn) = {for (n=0, nn, for (m=0, n, print1(T(n, m), ", ");); print(););} \\ _Michel Marcus_, May 02 2015
%K A033878 nonn,tabl,easy
%O A033878 0,5
%A A033878 _N. J. A. Sloane_.
%E A033878 Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003

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