OFFSET
0,5
LINKS
G. C. Greubel, Rows n = 0..50 of the triangle, flattened
FORMULA
T(n, k) = round( f(n)/(f(k)*f(n-k)) ), where f(n) = n*b(n)*f(n-1)/b(n-1), f(0) = f(1) = 1, b(n) = n^2 - 1, b(0) = b(1) = 1.
T(n, k) = round( f(n)/(f(k)*f(n-k)) ), where f(n) = (n-1)*(n+1)!, and f(0) = f(1) = 1.
T(n, n-k) = T(n, k).
EXAMPLE
Triangle begins as:
1;
1, 1;
1, 6, 1;
1, 8, 8, 1;
1, 8, 10, 8, 1;
1, 8, 10, 10, 8, 1;
1, 9, 12, 11, 12, 9, 1;
1, 10, 14, 14, 14, 14, 10, 1;
1, 10, 17, 18, 20, 18, 17, 10, 1;
1, 11, 20, 24, 28, 28, 24, 20, 11, 1;
1, 12, 24, 31, 40, 43, 40, 31, 24, 12, 1;
MATHEMATICA
f[n_]:= If[n<2, 1, (n-1)*(n+1)!];
T[n_, k_]:= Round[f[n]/(f[n-k]*f[k])];
Table[T[n, k], {n, 0, 14}, {k, 0, n}]//Flatten
PROG
(Magma)
f:= func< n | n le 1 select 1 else (n-1)*Factorial(n+1) >;
A141600:= func< n, k | Round(f(n)/(f(k)*f(n-k))) >;
[A141600(n, k): k in [0..n], n in [0..14]]; // G. C. Greubel, Sep 20 2024
(SageMath)
def f(n): return 1 if (n<2) else (n-1)*factorial(n+1)
def A141600(n, k): return round(f(n)/(f(k)*f(n-k)))
flatten([[A141600(n, k) for k in range(n+1)] for n in range(15)]) # G. C. Greubel, Sep 20 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula and Gary W. Adamson, Aug 21 2008
EXTENSIONS
Edited and new name by G. C. Greubel, Sep 20 2024
STATUS
approved