|
Search: id:A110488
|
|
|
| A110488 |
|
A number triangle based on the Catalan numbers. |
|
+0
3
|
|
| 1, 1, 1, 2, 2, 1, 5, 5, 3, 1, 14, 14, 10, 4, 1, 42, 42, 35, 17, 5, 1, 132, 132, 126, 74, 26, 6, 1, 429, 429, 462, 326, 137, 37, 7, 1, 1430, 1430, 1716, 1446, 726, 230, 50, 8, 1, 4862, 4862, 6435, 6441, 3858, 1434, 359, 65, 9, 1, 16796, 16796, 24310, 28770, 20532, 8952
(list; table; graph; listen)
|
|
|
OFFSET
|
0,4
|
|
|
COMMENT
|
Columns include A000108,A001700,A049027(n+1),A076025(n+1). Rows sums are A110489, diagonal sums are A110490.
|
|
FORMULA
|
T(n, k)=sum{j=0..n-k, (k-1)^j*C(2(n-k)+1, n-k-j)*2*(j+1)/(n-k+j+2)}; Column k has g.f. x^k*c(x)/(1-k*x*c(x)) where c(x) is the g.f. of A000108.
|
|
EXAMPLE
|
Rows begin
1;
1,1;
2,2,1;
5,5,3,1;
14,14,10,4,1;
42,42,35,17,5,1;
|
|
CROSSREFS
|
Sequence in context: A141751 A079222 A033184 this_sequence A134379 A108087 A123158
Adjacent sequences: A110485 A110486 A110487 this_sequence A110489 A110490 A110491
|
|
KEYWORD
|
easy,nonn,tabl
|
|
AUTHOR
|
Paul Barry (pbarry(AT)wit.ie), Jul 22 2005
|
|
|
Search completed in 0.002 seconds
|
