OFFSET
1,2
COMMENTS
The triangle can be constructed multiplying the triangle A(n,k)=n-k+1 (if 1<=k<=n, else 0) by the triangle B(n,k) =k (if 1<=k<=n, else 0).
Swapping the two triangles of this matrix product would generate A104634.
LINKS
G. C. Greubel, Rows n=1..100 of triangle, flattened
Isabel Cação, Helmuth R. Malonek, Maria Irene Falcão, and Graça Tomaz, Intrinsic Properties of a Non-Symmetric Number Triangle, J. Int. Seq., Vol. 26 (2023), Article 23.4.8.
FORMULA
G.f.: x*y/((1 - x)^3*(1 - x*y)^2). - Stefano Spezia, May 22 2023
EXAMPLE
First few rows of the triangle:
1;
3, 2;
6, 6, 3;
10, 12, 9, 4;
15, 20, 18, 12, 5;
21, 30, 30, 24, 15, 6;
28, 42, 45, 40, 30, 18, 7;
36, 56, 63, 60, 50, 36, 21, 8;
...
e.g. Col. 3 = 3 * (1, 3, 6, 10, 15...) = 3, 9, 18, 30, 45...
MAPLE
A104633 := proc(n, k) k*(k-n-1)*(k-n-2)/2 ; end proc:
seq(seq(A104633(n, k), k=1..n), n=1..16) ; # R. J. Mathar, Mar 03 2011
MATHEMATICA
Table[k*(k-n-1)*(k-n-2)/2, {n, 1, 20}, {k, 1, n}] // Flatten (* G. C. Greubel, Aug 12 2018 *)
PROG
(PARI) for(n=1, 20, for(k=1, n, print1(k*(k-n-1)*(k-n-2)/2, ", "))) \\ G. C. Greubel, Aug 12 2018
(Magma) [[k*(k-n-1)*(k-n-2)/2: k in [1..n]]: n in [1..20]]; // G. C. Greubel, Aug 12 2018
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Mar 18 2005
STATUS
approved