OFFSET
0,11
FORMULA
T(m,n) = (m+n-2)*(binomial(m+n-2,m) + binomial(m+n-2,n)).
EXAMPLE
For (m,n) = (3,1), there are T(3,1) = 4 paths:
(3,0), (0,1)
(0,1), (3,0)
(2,1), (1,0)
(1,0), (2,1).
Array T(m,n) begins
n/m 0 1 2 3 4 5 6 7 8 9
0 0 0 0 1 2 3 4 5 6 7
1 0 0 1 4 9 16 25 36 49 64
2 0 1 4 12 28 55 96 154 232 333
3 1 4 12 32 75 156 294 512 837 1300
4 2 9 28 75 180 392 784 1458 2550 4235
5 3 16 55 156 392 896 1890 3720 6897 12144
6 4 25 96 294 784 1890 4200 8712 17028 31603
7 5 36 154 512 1458 3720 8712 19008 39039 76076
8 6 49 232 837 2550 6897 17028 39039 84084 171600
9 7 64 333 1300 4235 12144 31603 76076 171600 366080
PROG
(Sage)
def T(m, n):
return (m+n-2)*(binomial(m+n-2, m) + binomial(m+n-2, n))
CROSSREFS
KEYWORD
tabl,nonn
AUTHOR
Steven Klee, Dec 19 2019
STATUS
approved