A365539 Array read by ascending antidiagonals: A(n,k) = [x^n] (1 + x^k)/((1 - x)^2*(1 - x^k)), with k > 0.

1, 4, 1, 9, 2, 1, 16, 5, 2, 1, 25, 8, 3, 2, 1, 36, 13, 6, 3, 2, 1, 49, 18, 9, 4, 3, 2, 1, 64, 25, 12, 7, 4, 3, 2, 1, 81, 32, 17, 10, 5, 4, 3, 2, 1, 100, 41, 22, 13, 8, 5, 4, 3, 2, 1, 121, 50, 27, 16, 11, 6, 5, 4, 3, 2, 1, 144, 61, 34, 21, 14, 9, 6, 5, 4, 3, 2, 1

Offset: 0

Author

Stefano Spezia, Sep 08 2023

Keywords

• nonn
• tabl

Examples

			Array begins:
   1,  1,  1,  1,  1,  1,  1, ...
   4,  2,  2,  2,  2,  2,  2, ...
   9,  5,  3,  3,  3,  3,  3, ...
  16,  8,  6,  4,  4,  4,  4, ...
  25, 13,  9,  7,  5,  5,  5, ...
  36, 18, 12, 10,  8,  6,  6, ...
  49, 25, 17, 13, 11,  9,  7, ...
  64, 32, 22, 16, 14, 12, 10, ...
  ...
		

Crossrefs

Cf. A000027 (main diagonal and superdiagonals), A000290 (k=1), A000982 (k=2), A008810 (k=3), A008811 (k=4), A008812 (k=5), A008813 (k=6), A008814 (k=7), A008815 (k=8), A008816 (k=9), A008817 (k=10).

Cf. A365540 (antidiagonal sums).

Programs

Mathematica

A[n_,k_]:=SeriesCoefficient[(1+x^k)/((1-x)^2*(1-x^k)),{x,0,n}]; Table[A[n-k,k],{n,0,12},{k,n}]//Flatten