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 A362302 #23 Apr 16 2023 09:48:49
%S A362302 1,1,1,1,1,1,1,1,1,1,1,1,1,0,1,1,1,1,-1,-3,1,1,1,1,-2,-7,-9,1,1,1,1,
%T A362302 -3,-11,-19,-9,1,1,1,1,-4,-15,-29,1,36,1,1,1,1,-5,-19,-39,31,211,225,
%U A362302 1,1,1,1,-6,-23,-49,81,526,1009,477,1,1,1,1,-7,-27,-59,151,981,2353,953,-819,1
%N A362302 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 A362302 Seiichi Manyama, <a href="/A362302/b362302.txt">Antidiagonals n = 0..139, flattened</a>
%F A362302 E.g.f. of column k: exp(x - k*x^3/6).
%F A362302 T(n,k) = T(n-1,k) - k * binomial(n-1,2) * T(n-3,k) for n > 2.
%F A362302 T(n,k) = n! * Sum_{j=0..floor(n/3)} (-k/6)^j / (j! * (n-3*j)!).
%e A362302 Square array begins:
%e A362302 1, 1, 1, 1, 1, 1, 1, ...
%e A362302 1, 1, 1, 1, 1, 1, 1, ...
%e A362302 1, 1, 1, 1, 1, 1, 1, ...
%e A362302 1, 0, -1, -2, -3, -4, -5, ...
%e A362302 1, -3, -7, -11, -15, -19, -23, ...
%e A362302 1, -9, -19, -29, -39, -49, -59, ...
%e A362302 1, -9, 1, 31, 81, 151, 241, ...
%o A362302 (PARI) T(n, k) = n!*sum(j=0, n\3, (-k/6)^j/(j!*(n-3*j)!));
%Y A362302 Columns k=0..2 give A000012, A351929, A362309.
%Y A362302 Main diagonal gives A362303.
%Y A362302 T(n,2*n) gives A362304.
%Y A362302 T(n,6*n) gives A362305.
%Y A362302 Cf. A362043, A362277.
%K A362302 sign,tabl
%O A362302 0,20
%A A362302 _Seiichi Manyama_, Apr 15 2023