OFFSET
1,3
FORMULA
T(n,k) = Sum_{j=1..n} binomial(j+k-1,k)*floor(n/j) = (Sum_{j=1..floor(sqrt(n))} [floor(n/j)*((k+1)*binomial(j+k-1,k)+binomial(floor(n/j)+k,k))] - floor(sqrt(n))^2*binomial(floor(sqrt(n))+k,k))/(k+1).
G.f. of column k: (1/(1 - x)) * Sum_{j>=1} x^j/(1 - x^j)^(k+1). - Seiichi Manyama, Oct 30 2023
EXAMPLE
Array begins:
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ...
3, 4, 5, 6, 7, 8, 9, 10, 11, 12, ...
5, 8, 12, 17, 23, 30, 38, 47, 57, 68, ...
8, 15, 26, 42, 64, 93, 130, 176, 232, 299, ...
10, 21, 42, 78, 135, 220, 341, 507, 728, 1015, ...
14, 33, 73, 149, 282, 500, 839, 1344, 2070, 3083, ...
16, 41, 102, 234, 493, 963, 1764, 3061, 5074, 8089, ...
PROG
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Chai Wah Wu, Oct 30 2023
STATUS
approved