OFFSET
1,3
LINKS
G. C. Greubel, Rows n = 1..25 of the triangle, flattened
FORMULA
T(n, k) = Product_{j=1..n} ( (k+1)^j - Sum_{i=0..k-1} (k+1)^i ).
T(n, k) = (1/k^n)*Product_{j=1..n} ( (k-1)*(k+1)^j + 1 ). - G. C. Greubel, Jan 02 2022
EXAMPLE
Triangle begins as:
1;
1, 10;
1, 140, 1419;
1, 5740, 242649, 3350536;
1, 700280, 165729267, 7853656384, 161827775045;
MATHEMATICA
T[n_, k_]:= (1/k^n)*Product[(k-1)*(k+1)^j +1, {j, n}];
Table[T[n, k], {n, 10}, {k, n}]//Flatten (* modified by G. C. Greubel, Jan 02 2022 *)
PROG
(Magma) A156286:= func< n, k | (&*[(k-1)*(k+1)^j + 1: j in [1..n]])/k^n >;
[A156286(n, k): k in [1..n], n in [1..10]]; // G. C. Greubel, Jan 02 2022
(Sage)
def A156286(n, k): return (1/k^n)*product( (k-1)*(k+1)^j +1 for j in (1..n) )
flatten([[A156286(n, k) for k in (1..n)] for n in (1..10)]) # G. C. Greubel, Jan 02 2022
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 07 2009
EXTENSIONS
Edited by G. C. Greubel, Jan 02 2022
STATUS
approved