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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 (list; table; graph; refs; listen; history; text; internal format)
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

Cf. A156173.

Sequence in context: A185544 A048882 A192357 * A049223 A308282 A223512

Adjacent sequences: A156283 A156284 A156285 * A156287 A156288 A156289

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula, Feb 07 2009

EXTENSIONS

Edited by G. C. Greubel, Jan 02 2022

STATUS

approved

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Last modified November 27 03:04 EST 2022. Contains 358362 sequences. (Running on oeis4.)