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 A118933 #6 Mar 07 2021 20:36:18
%S A118933 1,1,1,1,1,6,1,30,1,90,1,210,1,420,1260,1,756,11340,1,1260,56700,1,
%T A118933 1980,207900,1,2970,623700,1247400,1,4290,1621620,16216200,1,6006,
%U A118933 3783780,113513400,1,8190,8108100,567567000,1,10920,16216200,2270268000,3405402000
%N A118933 Triangle, read by rows, where T(n,k) = n!/(k!*(n-4*k)!*4^k) for n>=4*k>=0.
%C A118933 Row n contains 1+floor(n/4) terms. Row sums yield A118934. Given column vector V = A118935, then V is invariant under matrix product T*V = V, or, A118935(n) = Sum_{k=0..n} T(n,k)*A118935(k). Given C = Pascal's triangle and T = this triangle, then matrix product M = C^-1*T yields M(4n,n) = (4*n)!/(n!*4^n), 0 otherwise (cf. A100861 formula due to Paul Barry).
%H A118933 G. C. Greubel, <a href="/A118933/b118933.txt">Rows n = 0..150 of the triangle, flattened</a>
%F A118933 E.g.f.: A(x,y) = exp(x + y*x^4/4).
%e A118933 Triangle begins:
%e A118933 1;
%e A118933 1;
%e A118933 1;
%e A118933 1;
%e A118933 1, 6;
%e A118933 1, 30;
%e A118933 1, 90;
%e A118933 1, 210;
%e A118933 1, 420, 1260;
%e A118933 1, 756, 11340;
%e A118933 1, 1260, 56700;
%e A118933 1, 1980, 207900;
%e A118933 1, 2970, 623700, 1247400; ...
%t A118933 T[n_, k_]:= If[n<4*k, 0, n!/(4^k*k!*(n-4*k)!)];
%t A118933 Table[T[n, k], {n,0,20}, {k,0,n/4}]//Flatten (* _G. C. Greubel_, Mar 07 2021 *)
%o A118933 (PARI) T(n,k)=if(n<4*k,0,n!/(k!*(n-4*k)!*4^k))
%o A118933 (Sage)
%o A118933 f=factorial;
%o A118933 flatten([[0 if n<4*k else f(n)/(4^k*f(k)*f(n-4*k)) for k in [0..n/4]] for n in [0..20]]) # _G. C. Greubel_, Mar 07 2021
%o A118933 (Magma)
%o A118933 F:= Factorial;
%o A118933 [n lt 4*k select 0 else F(n)/(4^k*F(k)*F(n-4*k)): k in [0..Floor(n/4)], n in [0..20]]; // _G. C. Greubel_, Mar 07 2021
%Y A118933 Cf. A118934 (row sums), A118935 (invariant vector).
%Y A118933 Variants: A100861, A118931.
%K A118933 nonn,tabl
%O A118933 0,6
%A A118933 _Paul D. Hanna_, May 06 2006