A379587 Array read by ascending antidiagonals: A(n, k) = (k^n - 1)^2/(k - 1), with k >= 2.
0, 1, 0, 9, 2, 0, 49, 32, 3, 0, 225, 338, 75, 4, 0, 961, 3200, 1323, 144, 5, 0, 3969, 29282, 21675, 3844, 245, 6, 0, 16129, 264992, 348843, 97344, 9245, 384, 7, 0, 65025, 2389298, 5589675, 2439844, 335405, 19494, 567, 8, 0, 261121, 21516800, 89467563, 61027344, 12090125, 960000, 37303, 800, 9, 0
Offset: 0
Examples
The array begins as:
0, 0, 0, 0, 0, 0, ...
1, 2, 3, 4, 5, 6, ...
9, 32, 75, 144, 245, 384, ...
49, 338, 1323, 3844, 9245, 19494, ...
225, 3200, 21675, 97344, 335405, 960000, ...
961, 29282, 348843, 2439844, 12090125, 47073606, ...
...
Crossrefs
Programs
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Mathematica
A[n_,k_]:=(k^n-1)^2/(k-1); Table[A[n-k+2,k],{n,0,9},{k,2,n+2}]//Flatten
Formula
G.f. of column k: (1 - k)*x*(1 + k*x)/((1 - x)*(1 - k*x)*(1 - k^2*x)).
E.g.f. of column k: exp(x)*(1 - 2*exp((k-1)*x) + exp((k^2-1)*x))/(k - 1).
A(2, n) = A027620(n-2) for n > 1.