A133708 - OEIS

%I #9 Aug 08 2015 18:11:54

%S 0,0,1,69,1694,22932,208152,1413720,7697052,35194302,139687119,

%T 493127635,1577331756,4637757488,12679063488,32529562560,78917794128,

%U 182184724908,402332471541,853769650041,1747606106554,3462012537060,6656436729800,12452933493000

%N First differences of A047835.

%H T. D. Noe, <a href="/A133708/b133708.txt">Table of n, a(n) for n = 1..1003</a>

%F 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 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 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 Cf. A040977, A047819, A047835, A107915.

%K nonn

%O 1,4

%A _Peter Bala_, Sep 21 2007