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 A247591 #21 Nov 12 2023 12:08:09
%S A247591 1,1,3,16,126,1296,16071,228514,3607890,61891050,1135871490,
%T A247591 22049362440,448790912004,9512960347260,208858963314735,
%U A247591 4728736078065810,110006925920592810,2621619942885055530,63840054782606886630,1585094577104979776880,40054740803371374834780,1028483346608802276173280
%N A247591 Dimension of invariants of 2n-th tensor power of 6-dimensional irreducible representation of A_3.
%C A247591 The 6-dimensional representation is the usual representation of SO(6)=A_3.
%F A247591 a(n) = (-36*(n-1)*(2*n-3)*(2*n-1)*a(n-2) + 4*n*(2*n-1)*(5*n+7)*a(n-1)) / ((n+2)*(n+3)^2).
%F A247591 a(n) = (9*(n+1)*A005802(n)-(n+5)*A005802(n+1))*binomial(2*n,n)/(2*(n+1)*(n+2)). - _Mark van Hoeij_, Nov 12 2023
%e A247591 For 2n=6, there are 15 invariants corresponding to all ways of pairing the 6 indices with the metric tensor, plus one invariant which is the completely skew-symmetric 6-index tensor.
%t A247591 a[0] = 1; a[1] = 1; a[n_] := a[n] = (4*n*(2*n-1)*(5*n+7)*a[n-1] - 36*(n-1)*(2*n-3)*(2*n-1)*a[n-2]) / ((n+2)*(n+3)^2); Table[a[n], {n, 0, 21}]
%o A247591 (PARI) N=66; v=vector(N); v[1]=1; v[2]=1;
%o A247591 for(n=2, N-1, my(t=n+1); v[t] = (-36*(n-1)*(2*n-3)*(2*n-1)*v[t-2] + 4*n*(2*n-1)*(5*n+7)*v[t-1]) / ((n+2)*(n+3)^2) );
%o A247591 v \\ _Joerg Arndt_, Sep 20 2014
%Y A247591 Cf. A095922, A059710.
%K A247591 nonn
%O A247591 0,3
%A A247591 _Paul Zinn-Justin_, Sep 20 2014