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 A294082 #60 Mar 28 2018 14:18:53
%S A294082 1,1,1,1,2,1,1,4,3,1,1,14,9,4,1,1,184,75,16,5,1,1,33674,5553,244,25,6,
%T A294082 1,1,1133904604,30830259,59296,605,36,7,1,1,1285739649838492214,
%U A294082 950504839176825,3515956324,365425,1266,49,8,1
%N A294082 Square array read by antidiagonals: T(m,n) = T(m,n-1)^2 - T(m,n-2)^2 + T(m,n-2) with T(1,n) = 1, T(m,0) = 1, and T(m,1) = m.
%C A294082 The columns of T(n,m) enumerate the size of the set S(n) constructed recursively as follows: Let S(1) = {a_1, ..., a_m}, where a_i are arbitrary elements, and let P(S) be the set of pairs (s,t) where s,t are members of S and s is not equal to t. We define S(n+1) to be the union of S(n) and P(S(n)). For example Let S(1) = {a_1,a_2}, then S(2) = {a_1,a_2, (a_1,a_2),(a_2,a_1)} where (a_1,a_2) is the pairing of a_{1} and a_{2}. Furthermore S(2) = {a_1,a_2, (a_1,a_2),(a_2,a_1), (a_1,(a_1,a_2)), (a_1,(a_2,a_1)), ((a_1,a_2),a_1), ((a_2,a_1),a_1), (a_2,(a_1,a_2)), (a_2,(a_2,a_1)), ((a_1,a_2),a_2), ((a_2,a_1),a_2)((a_1,a_2), (a_2,a_1)) }.
%e A294082 Array begins:
%e A294082 =============================================================================
%e A294082 m\n| 0 1 2 3 4 5 6
%e A294082 ---|-------------------------------------------------------------------------
%e A294082 1 | 1 1 1 1 1 1 1
%e A294082 2 | 1 2 4 14 184 33674 1133904604
%e A294082 3 | 1 3 9 75 5553 30830259 950504839176825
%e A294082 4 | 1 4 16 244 59296 3515956324 12361948868759636656
%e A294082 5 | 1 5 25 605 365425 133535065205 17831613639170066626825
%e A294082 6 | 1 6 36 1266 1601496 2564787836526 6578136646389154911912156
%e A294082 7 | 1 7 49 2359 5562529 30941723313319 957390241597957573719482449
%e A294082 8 | 1 8 64 4040 16317568 266263009117064 70895990024073440521846863040
%e A294082 ...
%t A294082 t[n_, m_] := t[n -1, m]^2 - t[n -2, m]^2 + t[n -2, m]; t[0, m_] := 1; t[1, m_] := m; Table[ t[n -m +1, m], {n, 0, 8}, {m, n +1}] // Flatten
%t A294082 (* to produce the table *) Table[t[n, m], {m, 8}, {n, 0, 6}] // TableForm (* _Robert G. Wilson v_, Feb 09 2018 *)
%o A294082 (PARI) T(n, k) = if (k<0, 0, if (n==1, 1, if (k==0, 1, if (k==1, n, T(n, k-1)^2 - T(n, k-2)^2 + T(n, k-2)))));
%o A294082 tabl(nn) = for (n=1, nn , for (k=0, nn, print1(T(n, k), ", ")); print); \\ _Michel Marcus_, Mar 06 2018
%Y A294082 Cf. A000058, A166105.
%K A294082 nonn,easy,tabl
%O A294082 1,5
%A A294082 _David M. Cerna_, Feb 09 2018