|
|
A171150
|
|
Triangle related to T(x,2x).
|
|
0
|
|
|
1, 1, 1, 2, 3, 1, 3, 9, 7, 1, 6, 20, 28, 15, 1, 10, 50, 85, 75, 31, 1, 20, 105, 255, 294, 186, 63, 1, 35, 245, 651, 1029, 903, 441, 127, 1, 70, 504, 1736, 3108, 3612, 2568, 1016, 255, 1, 126, 1134, 4116, 9324, 12636, 11556, 6921, 2295, 511, 1, 252, 2310, 10290, 25080, 42120, 46035, 34605, 17930, 5110, 1023, 1
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Let the triangle T_(x,y)=T defined by T(0,0)=1, T(n,k)=0 if k<0 or if k>n, T(n,0)=x*T(n-1,0)+T(n-1,1), T(n,k)=T(n-1,k-1)+y*T(n-1,k)+T(n-1,k+1) for k>=1.
This triangle gives the coefficients of Sum_{k=0..n} T(n,k) where y=2x.
First column of T_(x,2x) is given by A126222.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
2, 3, 1;
3, 9, 7, 1;
6, 20, 28, 15, 1;
10, 50, 85, 75, 31, 1;
...
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|