A033878 Triangular array associated with Schroeder numbers.

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

Offset

0,5

Comments

Transpose of triangular array A132372. - Michel Marcus, May 02 2015

Links

Table of n, a(n) for n=0..54.

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: A050165 A330784 A198876 * A144061 A085792 A108123

Adjacent sequences: A033875 A033876 A033877 * A033879 A033880 A033881

Keyword

nonn,tabl,easy

Author

N. J. A. Sloane.

Extensions

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

Status

approved