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 A379459 #4 Jan 03 2025 02:03:22
%S A379459 2,4,8,12,36,52,48,192,368,472,240,1200,2880,4560,5504,1440,8640,
%T A379459 24960,47280,67408,78416,10080,70560,238560,527520,871584,1163232,
%U A379459 1320064,80640,645120,2499840,6330240,11926656,18031104,22997696,25637824,725760,6531840,28546560,81527040,172811520,292642560,415728960,513000000,564275648
%N A379459 Array read by downward antidiagonals: A(n,k) = A(n-1,k+1) + 2*(k+1)!*Sum_{j=0..k} A(n-1,j)/j! with A(0,k) = 2*(k+1)!, n >= 0, k >= 0.
%F A379459 Conjecture: A(n,0) = A006351(n+2).
%e A379459 Array begins:
%e A379459 ================================================================
%e A379459 n\k| 0 1 2 3 4 5 ...
%e A379459 ---+------------------------------------------------------------
%e A379459 0 | 2 4 12 48 240 1440 ...
%e A379459 1 | 8 36 192 1200 8640 70560 ...
%e A379459 2 | 52 368 2880 24960 238560 2499840 ...
%e A379459 3 | 472 4560 47280 527520 6330240 81527040 ...
%e A379459 4 | 5504 67408 871584 11926656 172811520 2649749760 ...
%e A379459 5 | 78416 1163232 18031104 292642560 4977020160 88700451840 ...
%e A379459 ...
%o A379459 (PARI) A(m, n=m)={my(r=vectorv(m+1), v=vector(n+m+1, k, 2*k!)); r[1] = v[1..n+1];
%o A379459 for(i=1, m, v=vector(#v-1, k, v[k+1] + 2*k!*sum(j=1, k, v[j]/(j-1)!)); r[1+i] = v[1..n+1]); Mat(r)}
%o A379459 { A(5) }
%Y A379459 Cf. A006351.
%K A379459 nonn,tabl
%O A379459 0,1
%A A379459 _Mikhail Kurkov_, Dec 23 2024