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A361475
Array read by ascending antidiagonals: A(n, k) = (k^n - 1)/(k - 1), with k >= 2.
1
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
0,4
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.
EXAMPLE
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, ...
...
MATHEMATICA
A[n_, k_]:=(k^n-1)/(k-1); Flatten[Table[A[n-k+2, k], {n, 0, 10}, {k, 2, n+2}]]
CROSSREFS
Cf. A003992, A361291 (k=2*n+1), A361476 (antidiagonal sums).
Cf. A000225 (k=2), A003462 (k=3), A002450 (k=4), A003463 (k=5), A003464 (k=6), A023000 (k=7), A023001 (k=8), A002452 (k=9), A002275 (k=10), A016123 (k=11).
Sequence in context: A010601 A176108 A110504 * A111246 A206306 A178124
KEYWORD
nonn,tabl
AUTHOR
Stefano Spezia, Mar 13 2023
STATUS
approved