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 A257614 #14 Mar 01 2022 05:32:37
%S A257614 1,2,2,4,28,4,8,244,244,8,16,1844,5856,1844,16,32,13260,101620,101620,
%T A257614 13260,32,64,93684,1511160,3455080,1511160,93684,64,128,657836,
%U A257614 20663388,91981880,91981880,20663388,657836,128,256,4609588,269011408,2121603436,4047202720,2121603436,269011408,4609588,256
%N A257614 Triangle read by rows: T(n, k) = t(n-k, k), where 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), and f(n) = 5*n + 2.
%H A257614 G. C. Greubel, <a href="/A257614/b257614.txt">Rows n = 0..50 of the triangle, flattened</a>
%F A257614 T(n, k) = t(n-k, k), where 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), and f(n) = 5*n + 2.
%F A257614 Sum_{k=0..n} T(n, k) = A008546(n).
%F A257614 From _G. C. Greubel_, Mar 01 2022: (Start)
%F A257614 t(k, n) = t(n, k).
%F A257614 T(n, n-k) = T(n, k).
%F A257614 t(0, n) = T(n, 0) = A000079(n). (End)
%e A257614 Array t(n,k) begins as:
%e A257614 1, 2, 4, 8, 16, ... A000079;
%e A257614 2, 28, 244, 1844, 13260, ...;
%e A257614 4, 244, 5856, 101620, 1511160, ...;
%e A257614 8, 1844, 101620, 3455080, 91981880, ...;
%e A257614 16, 13260, 1511160, 91981880, 4047202720, ...;
%e A257614 32, 93684, 20663388, 2121603436, 146321752612, ...;
%e A257614 64, 657836, 269011408, 44675623468, 4648698508440, ...;
%e A257614 Triangle T(n,k) begins as:
%e A257614 1;
%e A257614 2, 2;
%e A257614 4, 28, 4;
%e A257614 8, 244, 244, 8;
%e A257614 16, 1844, 5856, 1844, 16;
%e A257614 32, 13260, 101620, 101620, 13260, 32;
%e A257614 64, 93684, 1511160, 3455080, 1511160, 93684, 64;
%e A257614 128, 657836, 20663388, 91981880, 91981880, 20663388, 657836, 128;
%t A257614 t[n_, k_, p_, q_]:= t[n, k, p, q] = If[n<0 || k<0, 0, If[n==0 && k==0, 1, (p*k+q)*t[n-1,k,p,q] + (p*n+q)*t[n,k-1,p,q]]];
%t A257614 T[n_, k_, p_, q_]= t[n-k, k, p, q];
%t A257614 Table[T[n,k,5,2], {n,0,12}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 01 2022 *)
%o A257614 (Sage)
%o A257614 @CachedFunction
%o A257614 def t(n,k,p,q):
%o A257614 if (n<0 or k<0): return 0
%o A257614 elif (n==0 and k==0): return 1
%o A257614 else: return (p*k+q)*t(n-1,k,p,q) + (p*n+q)*t(n,k-1,p,q)
%o A257614 def A257614(n,k): return t(n-k,k,5,2)
%o A257614 flatten([[A257614(n,k) for k in (0..n)] for n in (0..12)]) # _G. C. Greubel_, Mar 01 2022
%Y A257614 Cf. A000079, A008546 (row sums), A142460, A257623.
%Y A257614 Cf. A038208, A256890, A257609, A257610, A257612, A257616, A257617, A257618, A257619.
%Y A257614 Similar sequences listed in A256890.
%K A257614 nonn,tabl
%O A257614 0,2
%A A257614 _Dale Gerdemann_, May 09 2015