A396403 Array read by ascending antidiagonals: A(n,k) = k^(n*(n - 1)/2) for k >= 0.

1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 2, 1, 1, 0, 1, 8, 3, 1, 1, 0, 1, 64, 27, 4, 1, 1, 0, 1, 1024, 729, 64, 5, 1, 1, 0, 1, 32768, 59049, 4096, 125, 6, 1, 1, 0, 1, 2097152, 14348907, 1048576, 15625, 216, 7, 1, 1, 0, 1, 268435456, 10460353203, 1073741824, 9765625, 46656, 343, 8, 1, 1

Offset

0,13

Links

Table of n, a(n) for n=0..65.

Example

The array begins as:
  1, 1,     1,        1,          1,           1, ...
  1, 1,     1,        1,          1,           1, ...
  0, 1,     2,        3,          4,           5, ...
  0, 1,     8,       27,         64,         125, ...
  0, 1,    64,      729,       4096,       15625, ...
  0, 1,  1024,    59049,    1048576,     9765625, ...
  0, 1, 32768, 14348907, 1073741824, 30517578125, ...
  ...

Mathematica

Unprotect[Power]; Power[0, 0]=1; Protect[Power]; A[n_, k_]:= k^(n*(n-1)/2); Table[A[n-k, k], {n, 0, 10}, {k, 0, n}]//Flatten

Crossrefs

Columns 0..11 give: A019560, A000012, A006125, A047656, A053763, A109345, A109354, A109493, A109966, A053764, A110147, A110195.

Rows 0..6 give: A000012, A001477, A000578, A008454, A010803, A122969.

Main diagonal gives A076113.

Antidiagonal sums give A396404.

Sequence in context: A275784 A331508 A097608 * A331126 A362899 A168261

Adjacent sequences: A396400 A396401 A396402 * A396404 A396405 A396406

Keyword

nonn,easy,tabl

Author

Stefano Spezia, May 24 2026

Status

approved