A103252 Array A000292(n)*A000217(k), read by antidiagonals.
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
Examples
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, ... ...
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.
- Joaquín Figueroa, Ivan Gonzalez, and Daniel Salinas-Arizmendi, A Novel Transfer Matrix Framework for Multiple Dirac Delta Potentials, arXiv:2503.23134 [quant-ph], 2025. See pp. 5, 9.
Programs
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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 *)
Formula
G.f.: x*y/((1 - x)^4*(1 - y)^3). - Stefano Spezia, May 21 2023
Extensions
More terms from Stefano Spezia, May 21 2023