OFFSET
0,2
LINKS
G. C. Greubel, Rows n = 0..15 of the triangle, flattened
FORMULA
T(n, k) = (n+2)!*(n*(n+1)*(2*n+1)/6)!/( (k^2)! * abs(2 + 2*k^2 - (n*(n + 1)*(2*n+1)/6))! ).
EXAMPLE
Triangle begins as:
1;
6, 1;
480, 2880, 1;
21840, 2882880, 18162144000, 40040;
MATHEMATICA
T[n_, k_]= (n+2)!*(n*(n+1)*(2*n+1)/6)!/((k^2)!*Abs[2 +2*k^2 -(n*(n + 1)*(2*n+1)/6)]!);
Table[T[n, k], {n, 0, 10}, {k, 0, n}]//Flatten
PROG
(Magma)
F:=Factorial;
A123147:= func< n, k | F(n+2)*F(Floor(n*(n+1)*(2*n+1)/6))/( F(k^2) * F(Abs(Floor(2 + 2*k^2 - n*(n+1)*(2*n+1)/6))) ) >;
[A123147(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Jul 16 2023
(SageMath)
f=factorial
def A123147(n, k): return f(n+2)*f(n*(n+1)*(2*n+1)/6)/(f(k^2)*f(abs(2 + 2*k^2 - (n*(n+1)*(2*n+1)/6))) )
flatten([[A123147(n, k) for k in range(n+1)] for n in range(11)]) # G. C. Greubel, Jul 16 2023
CROSSREFS
KEYWORD
AUTHOR
Roger L. Bagula, Oct 01 2006
EXTENSIONS
Edited by G. C. Greubel, Jul 16 2023
STATUS
approved