|
| |
|
|
A178301
|
|
Triangle T(n,k) = binomial(n,k)*binomial(n+k+1,n+1) read by rows, 0<=k<=n.
|
|
2
|
|
|
|
1, 1, 3, 1, 8, 10, 1, 15, 45, 35, 1, 24, 126, 224, 126, 1, 35, 280, 840, 1050, 462, 1, 48, 540, 2400, 4950, 4752, 1716, 1, 63, 945, 5775, 17325, 27027, 21021, 6435, 1, 80, 1540, 12320, 50050, 112112, 140140, 91520, 24310, 1, 99, 2376, 24024, 126126, 378378, 672672, 700128, 393822, 92378
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
COMMENTS
|
Antidiagonal sums are given by A113682. - Johannes W. Meijer, Mar 24 2013
|
|
|
LINKS
|
Table of n, a(n) for n=0..54.
|
|
|
FORMULA
|
T(n,k) = A007318(n,k) * A178300(n+1,k+1).
|
|
|
EXAMPLE
|
1;
1,3;
1,8,10;
1,15,45,35;
1,24,126,224,126;
1,35,280,840,1050,462;
1,48,540,2400,4950,4752,1716;
1,63,945,5775,17325,27027,21021,6435;
|
|
|
MAPLE
|
A178301 := proc(n, k)
binomial(n, k)*binomial(n+k+1, n+1) ;
end proc: # R. J. Mathar, Mar 24 2013
|
|
|
CROSSREFS
|
Cf. A007318, A047781 (row sums), A178300.
Sequence in context: A008298 A039692 A071815 * A120236 A049760 A019146
Adjacent sequences: A178298 A178299 A178300 * A178302 A178303 A178304
|
|
|
KEYWORD
|
easy,nonn,tabl
|
|
|
AUTHOR
|
Alford Arnold, May 30 2010
|
|
|
STATUS
|
approved
|
| |
|
|
