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A364870
Array read by ascending antidiagonals: A(n, k) = (n + k)^n, with k >= 0.
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
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
KEYWORD
nonn,easy,tabl
AUTHOR
Stefano Spezia, Aug 11 2023
STATUS
approved