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 A033878 Triangular array associated with Schroeder numbers. 2
 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, 698, 394, 1, 13, 82, 334, 978, 2126, 3218, 1806, 1, 15, 110, 526, 1838, 4942, 10286, 15310, 8558, 1, 17, 142, 778, 3142, 9922, 25150, 50746, 74614, 41586 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Transpose of triangular array A132372. - Michel Marcus, May 02 2015 LINKS E. Pergola and R. A. Sulanke, Schroeder Triangles, Paths and Parallelogram Polyominoes, J. Integer Sequences, 1 (1998), #98.1.7. EXAMPLE This triangle reads: 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   698   394 1  13  82   334  978   2126  3218   1806 1  15  110  526  1838  4942  10286  15310   558 1  17  142  778  3142  9922  25150  50746  74614  41586 PROG (PARI) lgs(n) = if( n<1, 1, sum( k=0, n, 2^k * binomial( n, k) * binomial( n, k-1)) / n) /* A006318 */ 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))))); tabl(nn) = {for (n=0, nn, for (m=0, n, print1(T(n, m), ", "); ); print(); ); } \\ Michel Marcus, May 02 2015 CROSSREFS Sequence in context: A199479 A050165 A198876 * A144061 A085792 A108123 Adjacent sequences:  A033875 A033876 A033877 * A033879 A033880 A033881 KEYWORD nonn,tabl,easy AUTHOR EXTENSIONS Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 23 2003 STATUS approved

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