A361475 Array read by ascending antidiagonals: A(n, k) = (k^n - 1)/(k - 1), with k >= 2.
0, 1, 0, 3, 1, 0, 7, 4, 1, 0, 15, 13, 5, 1, 0, 31, 40, 21, 6, 1, 0, 63, 121, 85, 31, 7, 1, 0, 127, 364, 341, 156, 43, 8, 1, 0, 255, 1093, 1365, 781, 259, 57, 9, 1, 0, 511, 3280, 5461, 3906, 1555, 400, 73, 10, 1, 0, 1023, 9841, 21845, 19531, 9331, 2801, 585, 91, 11, 1, 0
Offset: 0
Examples
The array begins: 0, 0, 0, 0, 0, ... 1, 1, 1, 1, 1, ... 3, 4, 5, 6, 7, ... 7, 13, 21, 31, 43, ... 15, 40, 85, 156, 259, ... ...
Crossrefs
Programs
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Mathematica
A[n_,k_]:=(k^n-1)/(k-1); Flatten[Table[A[n-k+2,k],{n,0,10},{k,2,n+2}]]
Formula
E.g.f. of column k: exp(x)*(exp((k-1)*x) - 1)/(k - 1).
E.g.f. of column k: 2*exp((k+1)*x/2)*sinh((k-1)*x/2)/(k - 1).
A(n, k) = Sum_{i=0..n-1} k^i.