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A156286
Triangle T(n, k) = (1/k^n)*Product_{j=1..n} ( (k-1)*(k+1)^j + 1 ), read by rows.
1
1, 1, 10, 1, 140, 1419, 1, 5740, 242649, 3350536, 1, 700280, 165729267, 7853656384, 161827775045, 1, 255602200, 452606628177, 92036999164096, 6040221703554625, 193317016162131576, 1, 279628806800, 4943822199577371, 5392815929021041024, 1352701610289354714125, 132670761753844630766736, 6731905265314349384346775
OFFSET
1,3
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
Cf. A156173.
Sequence in context: A185544 A048882 A192357 * A049223 A308282 A223512
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Feb 07 2009
EXTENSIONS
Edited by G. C. Greubel, Jan 02 2022
STATUS
approved