OFFSET
0,5
COMMENTS
It appears that the T(n,k) are always integers. This would follow from the conjectured prime factorization given in the comments section of A092143.
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n,k) = Product_{j=1..n} floor(n/j)!/((Product_{j=1..n-k} floor((n-k)/j)!)*(Product_{j=1..k} floor(k/j)!)).
T(n, 1) = A007955(n).
T(n, n-k) = T(n, k). - G. C. Greubel, Feb 06 2024
EXAMPLE
Triangle starts
1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 8, 12, 8, 1;
1, 5, 20, 20, 5, 1;
MATHEMATICA
PROG
(Magma)
A092143:= func< n |n eq 0 select 1 else (&*[Factorial(Floor(n/j)): j in [1..n]]) >;
[A129439(n, k): k in [0..n], n in [0..13]]; // G. C. Greubel, Feb 06 2024
(SageMath)
def A092143(n): return product(factorial(n//j) for j in range(1, n+1))
flatten([[A129439(n, k) for k in range(n+1)] for n in range(14)]) # G. C. Greubel, Feb 06 2024
CROSSREFS
KEYWORD
AUTHOR
Peter Bala, Apr 15 2007
STATUS
approved