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%I #10 Aug 12 2023 00:55:05
%S 1,1,1,4,2,1,27,9,3,1,256,64,16,4,1,3125,625,125,25,5,1,46656,7776,
%T 1296,216,36,6,1,823543,117649,16807,2401,343,49,7,1,16777216,2097152,
%U 262144,32768,4096,512,64,8,1,387420489,43046721,4782969,531441,59049,6561,729,81,9,1
%N Array read by ascending antidiagonals: A(n, k) = (n + k)^n, with k >= 0.
%F E.g.f. of k-th column: LambertW(-x)^k/(x^k*(1 + LambertW(-x))).
%e The array begins:
%e 1, 1, 1, 1, 1, 1, ...
%e 1, 2, 3, 4, 5, 6, ...
%e 4, 9, 16, 25, 36, 49, ...
%e 27, 64, 125, 216, 343, 512, ...
%e 256, 625, 1296, 2401, 4096, 6561, ...
%e 3125, 7776, 16807, 32768, 59049, 100000, ...
%e ...
%t A[n_,k_]:=(n+k)^n; Join[{1},Table[A[n-k,k],{n,9},{k,0,n}]]//Flatten
%Y 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.
%K nonn,easy,tabl
%O 0,4
%A _Stefano Spezia_, Aug 11 2023