A298484 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is defined by the following: A(1,k) = k and A(n,k) = A(n-1,k)*(A(n-1,k)+1) for n > 1.

1, 2, 2, 3, 6, 6, 4, 12, 42, 42, 5, 20, 156, 1806, 1806, 6, 30, 420, 24492, 3263442, 3263442, 7, 42, 930, 176820, 599882556, 10650056950806, 10650056950806, 8, 56, 1806, 865830, 31265489220, 359859081592975692, 113423713055421844361000442, 113423713055421844361000442

Offset

1,2

Links

Seiichi Manyama, Antidiagonals n = 1..13, flattened

Example

Square array begins:
      1,       2,         3,           4,           5,              6, ...
      2,       6,        12,          20,          30,             42, ...
      6,      42,       156,         420,         930,           1806, ...
     42,    1806,     24492,      176820,      865830,        3263442, ...
   1806, 3263442, 599882556, 31265489220, 74966245730, 10650056950806, ...

Mathematica

A[1, k_?Positive] := k; A[n_?Positive, k_?Positive] := A[n, k] = A[n - 1, k]*(A[n - 1, k] + 1); Table[A[n - k + 1, k], {n, 1, 9}, {k, n, 1, -1}] // Flatten (* Jean-François Alcover, Feb 05 2018 *)

Crossrefs

Columns k=1..3 give A007018(n-1), A007018, A004168(n-1).

Rows n=1..3 give A000027, A002378, A169938.

Sequence in context: A179661 A178888 A068424 * A139359 A082481 A136573

Adjacent sequences: A298481 A298482 A298483 * A298485 A298486 A298487

Keyword

nonn,tabl

Author

Seiichi Manyama, Jan 20 2018

Status

approved