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 A257612 #33 Mar 21 2022 03:04:49
%S A257612 1,2,2,4,24,4,8,184,184,8,16,1216,3680,1216,16,32,7584,53824,53824,
%T A257612 7584,32,64,46208,674752,1507072,674752,46208,64,128,278912,7764096,
%U A257612 33244544,33244544,7764096,278912,128,256,1677312,84892672,636233728,1196803584,636233728,84892672,1677312,256
%N A257612 Triangle read by rows: T(n,k) = t(n-k, k); t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 4*x + 2.
%C A257612 Corresponding entries in this triangle and in A060187 differ only by powers of 2. - _F. Chapoton_, Nov 04 2020
%H A257612 G. C. Greubel, <a href="/A257612/b257612.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A257612 T(n,k) = t(n-k, k); t(0,0) = 1, t(n,m) = 0 if n < 0 or m < 0, else t(n,m) = f(m)*t(n-1,m) + f(n)*t(n,m-1), where f(x) = 4*x + 2.
%F A257612 Sum_{k=0..n} T(n,k) = A047053(n).
%F A257612 T(n, k) = (a*k + b)*T(n-1, k) + (a*(n-k) + b)*T(n-1, k-1), with T(n, 0) = 1, a = 4, and b = 2. - _G. C. Greubel_, Mar 20 2022
%e A257612 Triangle begins as:
%e A257612 1;
%e A257612 2, 2;
%e A257612 4, 24, 4;
%e A257612 8, 184, 184, 8;
%e A257612 16, 1216, 3680, 1216, 16;
%e A257612 32, 7584, 53824, 53824, 7584, 32;
%e A257612 64, 46208, 674752, 1507072, 674752, 46208, 64;
%e A257612 128, 278912, 7764096, 33244544, 33244544, 7764096, 278912, 128;
%t A257612 T[n_, k_, a_, b_]:= T[n, k, a, b]= If[k<0 || k>n, 0, If[n==0, 1, (a*(n-k)+b)*T[n-1, k-1, a, b] + (a*k+b)*T[n-1, k, a, b]]];
%t A257612 Table[T[n,k,4,2], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 20 2022 *)
%o A257612 (PARI) f(x) = 4*x + 2;
%o A257612 T(n, k) = t(n-k, k);
%o A257612 t(n, m) = if (!n && !m, 1, if (n < 0 || m < 0, 0, f(m)*t(n-1,m) + f(n)*t(n,m-1)));
%o A257612 tabl(nn) = for (n=0, nn, for (k=0, n, print1(T(n, k), ", ");); print();); \\ _Michel Marcus_, May 06 2015
%o A257612 (Sage)
%o A257612 def T(n,k,a,b): # A257612
%o A257612 if (k<0 or k>n): return 0
%o A257612 elif (n==0): return 1
%o A257612 else: return (a*k+b)*T(n-1,k,a,b) + (a*(n-k)+b)*T(n-1,k-1,a,b)
%o A257612 flatten([[T(n,k,4,2) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 20 2022
%Y A257612 Cf. A047053 (row sums), A060187, A142459, A257621.
%Y A257612 Cf. A038208, A256890, A257609, A257610, A257614, A257616, A257617, A257618, A257619.
%Y A257612 See similar sequences listed in A256890.
%K A257612 nonn,tabl
%O A257612 0,2
%A A257612 _Dale Gerdemann_, May 06 2015