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A103252
Array A000292(n)*A000217(k), read by antidiagonals.
1
1, 4, 3, 10, 12, 6, 20, 30, 24, 10, 35, 60, 60, 40, 15, 56, 105, 120, 100, 60, 21, 84, 168, 210, 200, 150, 84, 28, 120, 252, 336, 350, 300, 210, 112, 36, 165, 360, 504, 560, 525, 420, 280, 144, 45, 220, 495, 720, 840, 840, 735, 560, 360, 180, 55
OFFSET
1,2
LINKS
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)^4*(1 - y)^3). - Stefano Spezia, May 21 2023
EXAMPLE
Array begins
1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
4, 12, 24, 40, 60, 84, 112, 144, 180, 220, ...
10, 30, 60, 100, 150, 210, 280, 360, 450, 550, ...
20, 60, 120, 200, 300, 420, 560, 720, 900, 1100, ...
35, 105, 210, 350, 525, 735, 980, 1260, 1575, 1925, ...
...
MATHEMATICA
A[n_, k_]:=Binomial[n+2, 3]Binomial[k+1, 2]; Table[A[n-k+1, k], {n, 10}, {k, n}]//Flatten (* Stefano Spezia, May 21 2023 *)
CROSSREFS
Cf. A000579 (antidiagonal sums).
Main diagonal gives A004302.
Sequence in context: A299325 A316196 A081617 * A065763 A185730 A205965
KEYWORD
nonn,tabl,easy
AUTHOR
Gary W. Adamson, Mar 20 2005
EXTENSIONS
More terms from Stefano Spezia, May 21 2023
STATUS
approved