This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A362043 #24 Apr 16 2023 09:48:55
%S A362043 1,1,1,1,1,1,1,1,1,1,1,1,1,2,1,1,1,1,3,5,1,1,1,1,4,9,11,1,1,1,1,5,13,
%T A362043 21,31,1,1,1,1,6,17,31,81,106,1,1,1,1,7,21,41,151,351,337,1,1,1,1,8,
%U A362043 25,51,241,736,1233,1205,1,1,1,1,9,29,61,351,1261,2689,5769,5021,1
%N A362043 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..floor(n/3)} (k/6)^j * binomial(n-2*j,j)/(n-2*j)!.
%H A362043 Seiichi Manyama, <a href="/A362043/b362043.txt">Antidiagonals n = 0..139, flattened</a>
%F A362043 E.g.f. of column k: exp(x + k*x^3/6).
%F A362043 T(n,k) = T(n-1,k) + k * binomial(n-1,2) * T(n-3,k) for n > 2.
%F A362043 T(n,k) = n! * Sum_{j=0..floor(n/3)} (k/6)^j / (j! * (n-3*j)!).
%e A362043 Square array begins:
%e A362043 1, 1, 1, 1, 1, 1, 1, ...
%e A362043 1, 1, 1, 1, 1, 1, 1, ...
%e A362043 1, 1, 1, 1, 1, 1, 1, ...
%e A362043 1, 2, 3, 4, 5, 6, 7, ...
%e A362043 1, 5, 9, 13, 17, 21, 25, ...
%e A362043 1, 11, 21, 31, 41, 51, 61, ...
%e A362043 1, 31, 81, 151, 241, 351, 481, ...
%o A362043 (PARI) T(n, k) = n!*sum(j=0, n\3, (k/6)^j/(j!*(n-3*j)!));
%Y A362043 Columns k=0..2 give A000012, A190865, A001470.
%Y A362043 Main diagonal gives A362173.
%Y A362043 T(n,2*n) gives A362300.
%Y A362043 T(n,6*n) gives A362301.
%Y A362043 Cf. A359762, A362302.
%K A362043 nonn,tabl
%O A362043 0,14
%A A362043 _Seiichi Manyama_, Apr 15 2023