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 A362903 #12 Oct 15 2024 17:29:25
%S A362903 1,1,1,1,2,1,1,4,3,1,1,8,11,4,1,1,16,43,24,5,1,1,32,171,176,46,6,1,1,
%T A362903 64,683,1376,611,80,7,1,1,128,2731,10944,9281,1864,130,8,1,1,256,
%U A362903 10923,87424,146445,54384,5161,200,9,1,1,512,43691,699136,2334181,1696352,285939,13184,295,10,1
%N A362903 Array read by antidiagonals: T(n,k) is the number of nonisomorphic k-tuples of involutions on a (2n)-set that pairwise commute.
%C A362903 Two involutions x,y commute if x*y = y*x. Isomorphism is up to permutation of the elements of the (2n)-set. T(n,k) also gives the values for a (2n+1)-set.
%H A362903 Andrew Howroyd, <a href="/A362903/b362903.txt">Table of n, a(n) for n = 0..1325</a> (first 51 antidiagonals)
%F A362903 G.f. of column k: 1/((1 - x)*Product_{j=0..k-1} (1 - x^(2^j))^A022166(k,j+1)).
%e A362903 Array begins:
%e A362903 ======================================================
%e A362903 n/k| 0 1 2 3 4 5 6 ...
%e A362903 ---+--------------------------------------------------
%e A362903 0 | 1 1 1 1 1 1 1 ...
%e A362903 1 | 1 2 4 8 16 32 64 ...
%e A362903 2 | 1 3 11 43 171 683 2731 ...
%e A362903 3 | 1 4 24 176 1376 10944 87424 ...
%e A362903 4 | 1 5 46 611 9281 146445 2334181 ...
%e A362903 5 | 1 6 80 1864 54384 1696352 53885632 ...
%e A362903 6 | 1 7 130 5161 285939 17562679 1110290303 ...
%e A362903 7 | 1 8 200 13184 1372224 165343616 20774749952 ...
%e A362903 8 | 1 9 295 31532 6101080 1436647664 358238974304 ...
%e A362903 ...
%o A362903 (PARI) \\ B(n, k) is A022166.
%o A362903 B(n, k)={polcoef(x^k/prod(j=0, k, 1-2^j*x + O(x*x^n)), n)}
%o A362903 C(k,n) = Vec(1/prod(j=0, min(k-1, logint(n, 2)), (1 - x^(2^j) + O(x*x^n))^B(k,j+1), 1 - x + O(x*x^n)))
%o A362903 M(n,m=n) = Mat(vector(m+1, k, C(k-1, n)~))
%o A362903 { my(A=M(7)); for(i=1, #A, print(A[i,])) }
%Y A362903 Columns k=0..3 are A000012, A000027(n-1), A001752, A362904.
%Y A362903 Rows n=1..3 are A000079, A007583, A103334(n+1).
%Y A362903 Cf. A022166, A362648, A362824, A362826.
%K A362903 nonn,tabl
%O A362903 0,5
%A A362903 _Andrew Howroyd_, May 11 2023