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 A133708 #9 Aug 08 2015 18:11:54
%S A133708 0,0,1,69,1694,22932,208152,1413720,7697052,35194302,139687119,
%T A133708 493127635,1577331756,4637757488,12679063488,32529562560,78917794128,
%U A133708 182184724908,402332471541,853769650041,1747606106554,3462012537060,6656436729800,12452933493000
%N A133708 First differences of A047835.
%H A133708 T. D. Noe, <a href="/A133708/b133708.txt">Table of n, a(n) for n = 1..1003</a>
%F A133708 In terms of Vandermonde determinants, a(n) = 1/864*sum {1 <= x_1,x_2,x_3 <= n} (x_1*x_2*x_3)^2*(det V(x_1,x_2,x_3))^2 = 1/864 *sum {1 <= i,j,k <= n} (i*j*k*(i-j)(i-k)(j-k))^2, where V(x_1,x_2,x_3) is the Vandermonde matrix of order 3. a(n) = (n-2)*(n-1)^2*n^3*(n+1)^3*(n+2)^2*(n+3)*(n^2+n+3)*(2n+1)/108864000.
%F A133708 Empirical G.f.: x^3*(x+1)*(x^8+52*x^7+658*x^6+2890*x^5+4810*x^4+2890*x^3+658*x^2+52*x+1)/(x-1)^16. [_Colin Barker_, Jun 06 2012]
%t A133708 Join[{0,0,1},Differences[Table[Product[Times@@((i+Range[4,7])/(i+Range[0,3])),{i,n}],{n,0,30}]]] (* _Harvey P. Dale_, Aug 08 2015 *)
%Y A133708 Cf. A040977, A047819, A047835, A107915.
%K A133708 nonn
%O A133708 1,4
%A A133708 _Peter Bala_, Sep 21 2007