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 A118931 #8 Jun 06 2021 15:31:16
%S A118931 1,1,1,1,2,1,8,1,20,1,40,40,1,70,280,1,112,1120,1,168,3360,2240,1,240,
%T A118931 8400,22400,1,330,18480,123200,1,440,36960,492800,246400,1,572,68640,
%U A118931 1601600,3203200,1,728,120120,4484480,22422400,1,910,200200,11211200,112112000,44844800
%N A118931 Triangle, read by rows, where T(n,k) = n!/(k!*(n-3*k)!*3^k) for n>=3*k>=0.
%C A118931 Row n contains 1+floor(n/3) terms. Row sums yield A001470. Given column vector V = A118932, then V is invariant under matrix product T*V = V, or, A118932(n) = Sum_{k=0..n} T(n,k)*A118932(k). Given C = Pascal's triangle and T = this triangle, then matrix product M = C^-1*T yields M(3n,n) = (3*n)!/(n!*3^n), 0 otherwise (cf. A100861 formula due to Paul Barry).
%H A118931 G. C. Greubel, <a href="/A118931/b118931.txt">Rows n = 0..150 of the triangle, flattened</a>
%F A118931 E.g.f.: A(x,y) = exp(x + y*x^3/3).
%e A118931 Triangle T begins:
%e A118931 1;
%e A118931 1;
%e A118931 1;
%e A118931 1, 2;
%e A118931 1, 8;
%e A118931 1, 20;
%e A118931 1, 40, 40;
%e A118931 1, 70, 280;
%e A118931 1, 112, 1120;
%e A118931 1, 168, 3360, 2240;
%e A118931 1, 240, 8400, 22400;
%e A118931 1, 330, 18480, 123200;
%e A118931 1, 440, 36960, 492800, 246400;
%p A118931 Trow := n -> seq(n!/(j!*(n - 3*j)!*(3^j)), j = 0..n/3):
%p A118931 seq(Trow(n), n = 0..14); # _Peter Luschny_, Jun 06 2021
%t A118931 T[n_,k_]:= If[n<3*k, 0, n!/(3^k*k!*(n-3*k)!)];
%t A118931 Table[T[n,k], {n,0,20}, {k,0,Floor[n/3]}]//Flatten (* _G. C. Greubel_, Mar 07 2021 *)
%o A118931 (PARI) T(n,k)=if(n<3*k,0,n!/(k!*(n-3*k)!*3^k))
%o A118931 (Sage)
%o A118931 f=factorial;
%o A118931 flatten([[0 if n<3*k else f(n)/(3^k*f(k)*f(n-3*k)) for k in [0..n/3]] for n in [0..20]]) # _G. C. Greubel_, Mar 07 2021
%o A118931 (Magma)
%o A118931 F:= Factorial;
%o A118931 [n lt 3*k select 0 else F(n)/(3^k*F(k)*F(n-3*k)): k in [0..Floor(n/3)], n in [0..20]]; // _G. C. Greubel_, Mar 07 2021
%Y A118931 Cf. A001470 (row sums), A118932 (invariant vector).
%Y A118931 Variants: A100861, A118933.
%K A118931 nonn,tabl
%O A118931 0,5
%A A118931 _Paul D. Hanna_, May 06 2006