A364870 Array read by ascending antidiagonals: A(n, k) = (n + k)^n, with k >= 0.

1, 1, 1, 4, 2, 1, 27, 9, 3, 1, 256, 64, 16, 4, 1, 3125, 625, 125, 25, 5, 1, 46656, 7776, 1296, 216, 36, 6, 1, 823543, 117649, 16807, 2401, 343, 49, 7, 1, 16777216, 2097152, 262144, 32768, 4096, 512, 64, 8, 1, 387420489, 43046721, 4782969, 531441, 59049, 6561, 729, 81, 9, 1

Offset

0,4

Links

Table of n, a(n) for n=0..54.

Formula

E.g.f. of k-th column: LambertW(-x)^k/(x^k*(1 + LambertW(-x))).

Example

The array begins:
     1,    1,     1,     1,     1,      1, ...
     1,    2,     3,     4,     5,      6, ...
     4,    9,    16,    25,    36,     49, ...
    27,   64,   125,   216,   343,    512, ...
   256,  625,  1296,  2401,  4096,   6561, ...
  3125, 7776, 16807, 32768, 59049, 100000, ...
  ...

Mathematica

A[n_, k_]:=(n+k)^n; Join[{1}, Table[A[n-k, k], {n, 9}, {k, 0, n}]]//Flatten

Crossrefs

Cf. A000012 (n=0), A000169, A000272, A000312 (k=0), A007830 (k=3), A008785 (k=4), A008786 (k=5), A008787 (k=6), A031973 (antidiagonal sums), A052746 (2nd superdiagonal), A052750, A062971 (main diagonal), A079901 (read by descending antidiagonals), A085527 (1st superdiagonal), A085528 (1st subdiagonal), A085532, A099753.

Sequence in context: A239894 A152406 A105623 * A158835 A236961 A245958

Adjacent sequences: A364867 A364868 A364869 * A364871 A364872 A364873

Keyword

nonn,easy,tabl

Author

Stefano Spezia, Aug 11 2023

Status

approved