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 A361600 #30 Mar 26 2023 11:14:32
%S A361600 1,1,2,1,2,5,1,2,7,16,1,2,9,34,65,1,2,11,58,209,326,1,2,13,88,473,
%T A361600 1546,1957,1,2,15,124,881,4626,13327,13700,1,2,17,166,1457,10526,
%U A361600 52537,130922,109601,1,2,19,214,2225,20326,145867,677594,1441729,986410
%N A361600 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = n! * Sum_{j=0..n} binomial(n+(k-1)*j,k*j)/j!.
%H A361600 Seiichi Manyama, <a href="/A361600/b361600.txt">Antidiagonals n = 0..139, flattened</a>
%F A361600 E.g.f. of column k: exp( x/(1 - x)^k ) / (1-x).
%F A361600 T(n,k) = Sum_{j=0..n} (n+(k-1)*j)!/(k*j)! * binomial(n,j).
%e A361600 Square array begins:
%e A361600 1, 1, 1, 1, 1, 1, ...
%e A361600 2, 2, 2, 2, 2, 2, ...
%e A361600 5, 7, 9, 11, 13, 15, ...
%e A361600 16, 34, 58, 88, 124, 166, ...
%e A361600 65, 209, 473, 881, 1457, 2225, ...
%e A361600 326, 1546, 4626, 10526, 20326, 35226, ...
%o A361600 (PARI) T(n, k) = n!*sum(j=0, n, binomial(n+(k-1)*j, k*j)/j!);
%Y A361600 Columns k=0..3 give A000522, A002720, A361598, A361599.
%Y A361600 Main diagonal gives A361607.
%Y A361600 Cf. A293012.
%K A361600 nonn,tabl
%O A361600 0,3
%A A361600 _Seiichi Manyama_, Mar 17 2023