OFFSET
1,2
COMMENTS
This summation over columns of the Narayana triangle could also be defined as a multiplication
of the Narayana triangle from the left by the lower-left triangle represented by the all-1 sequence A000012.
FORMULA
Row sums: sum_{m=1..n} T(n,m) = A014138(n).
EXAMPLE
First few rows of the triangle are:
1;
2, 1;
3, 4, 1;
4, 10, 7, 1;
5, 20, 27, 11, 1;
6, 35, 77, 61, 16, 1;
...
PROG
(Python)
from sympy import binomial
def A001263(n, m):
return binomial(n-1, m-1)*binomial(n, m-1)//m
def A104711(n, m):
a = 0
for k in range(m, n+1):
a += A001263(k, m)
return a
print([A104711(n, m) for n in range(20) for m in range(1, n+1)]) # R. J. Mathar, Oct 11 2009
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Mar 19 2005
EXTENSIONS
Extended by R. J. Mathar, Oct 11 2009
STATUS
approved