A033878 - OEIS

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

(list; table; graph; refs; listen; history; text; internal format)

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 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