|
Search: id:A068555
|
|
|
| A068555 |
|
Triangle read by rows in which row n contains (2i)!*(2j)!/(i!*j!*(i+j)!) for i+j=n, i=0..n. |
|
+0
3
|
|
| 1, 2, 2, 6, 2, 6, 20, 4, 4, 20, 70, 10, 6, 10, 70, 252, 28, 12, 12, 28, 252, 924, 84, 28, 20, 28, 84, 924, 3432, 264, 72, 40, 40, 72, 264, 3432, 12870, 858, 198, 90, 70, 90, 198, 858, 12870, 48620, 2860, 572, 220, 140, 140, 220, 572, 2860, 48620, 184756, 9724
(list; table; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
REFERENCES
|
Suggested by R. K. Guy and Cal Long, Feb 22, 2002
Larcombe, Peter J.; French, David R. On the integrality of the Catalan-Larcombe-French sequence 1,8,80,896,10816,.... Proceedings of the Thirty-second Southeastern International Conference on Combinatorics, Graph Theory and Computing (Baton Rouge, LA, 2001). Congr. Numer. 148 (2001), 65-91. MR1887375
|
|
LINKS
|
Ira Gessel, Rational functions with nonnegative power series, (slides).
Ira Gessel, Super ballot numbers.
|
|
FORMULA
|
The square array defined by f := (a, b)->add(binomial(2*a, k)*binomial(2*b, a+b-k)*(-1)^(a+b-k), k=0..2*a); and read by antidiagonals gives a signed version.
|
|
EXAMPLE
|
1; 2,2; 6,2,6; 20,4,4,20; ...
|
|
MATHEMATICA
|
Flatten[ Table[ Table[ (2i)!*(2(n - i))!/(i!*(n - i)!*n!), {i, 0, n}], {n, 0, 9}]]
|
|
PROGRAM
|
(PARI) a(n, k)=if(n<0|k<0, 0, (2*n)!*(2*k)!/n!/k!/(n+k)!)
|
|
CROSSREFS
|
Apart perhaps from signs, diagonals give A000984, A002420, A078718.
Sequence in context: A093656 A084426 A138061 this_sequence A028330 A071052 A096869
Adjacent sequences: A068552 A068553 A068554 this_sequence A068556 A068557 A068558
|
|
KEYWORD
|
tabl,easy,nice,nonn
|
|
AUTHOR
|
njas, Mar 23 2002
|
|
EXTENSIONS
|
More terms from John W. Layman (layman(AT)math.vt.edu) and Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 27 2002
|
|
|
Search completed in 0.002 seconds
|
