OFFSET
1,2
COMMENTS
m ranges from 2n-1 to n^2.
First column is A068087.
EXAMPLE
Triangle begins:
----|------------------------------------------------------------
n\m | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
----|------------------------------------------------------------
1 | 1
2 | - - 4 1
3 | - - - - 81 78 36 9 1
4 | - - - - - - 4096 8424 9552 7464 4272 1812 560 120 16 1
PROG
(Python)
from math import comb as binomial
def f(x, a, b, k):
if b == k == 0:
return 1
if b == 0 or k == 0:
return 0
if x == a:
return sum(binomial(a, n) * f(x, x, b - 1, k - n) for n in range(1, a + 1))
return sum(binomial(b, n) * f(x, x, n, k2) * f(n, b, a - x, k - k2)
for n in range(1, b + 1) for k2 in range(0, k + 1) )
def a(n, m):
return f(1, n, n, m)
for n in range(1, 5):
print([a(n, m) for m in range(1, n * n + 1)])
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Thomas Dybdahl Ahle, Feb 16 2015
STATUS
approved