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 A335095 #24 Apr 29 2021 04:34:32
%S A335095 0,0,1,0,1,2,0,1,8,3,0,1,34,71,4,0,1,152,1891,744,5,0,1,706,55511,
%T A335095 164196,9129,6,0,1,3368,1745731,41625144,20760741,129072,7,0,1,16354,
%U A335095 57365351,11575291716,56246975289,3616621254,2071215,8
%N A335095 Square array T(n,k), n>=0, k>=0, read by antidiagonals: T(n,k) = ((2n+1)!!)^k * Sum_{j=1..n} 1/(2*j+1)^k.
%F A335095 T(0,k) = 0, T(1,k) = 1 and T(n,k) = ((2*n-1)^k+(2*n+1)^k) * T(n-1,k) - (2*n-1)^(2*k) * T(n-2, k) for n>1.
%e A335095 Square array begins:
%e A335095 0, 0, 0, 0, 0, ...
%e A335095 1, 1, 1, 1, 1, ...
%e A335095 2, 8, 34, 152, 706, ...
%e A335095 3, 71, 1891, 55511, 1745731, ...
%e A335095 4, 744, 164196, 41625144, 11575291716, ...
%t A335095 T[n_, k_] := ((2*n + 1)!!)^k * Sum[1/(2*j + 1)^k, {j, 1, n}]; Table[T[k, n - k], {n, 0, 8}, {k, 0, n}] // Flatten (* _Amiram Eldar_, Apr 29 2021 *)
%o A335095 (PARI) {T(n, k) = prod(j=1, n, 2*j+1)^k*sum(j=1, n, 1/(2*j+1)^k)}
%Y A335095 Column k=0..4 give A001477, A334670, A335090, A335091, A335092.
%Y A335095 Rows n=0-2 give: A000004, A000012, A074606.
%Y A335095 Main diagonal gives A335096.
%Y A335095 Cf. A291656.
%K A335095 nonn,tabl
%O A335095 0,6
%A A335095 _Seiichi Manyama_, Sep 12 2020