A203695 - OEIS

%I #8 Jan 14 2013 08:30:27

%S 1,10,16650,24928779600,111827645954579880000,

%T 3822731887490658669088662984000000,

%U 2132112202139633769017736141415928803125840000000000

%N Vandermonde sequence using x^2 + y^2 applied to the first n triangular numbers: 1,3,6,10,...,n(n+1)/2.

%C See A093883 for a discussion and guide to related sequences.

%t f[j_] := j (j + 1)/2; z = 11;

%t u[n_] := Product[f[j]^2 + f[k]^2, {j, 1, k - 1}]

%t v[n_] := Product[u[n], {k, 2, n}]

%t Table[v[n], {n, 1, z}]          (* A203695 *)

%t Table[v[n + 1]/v[n], {n, 1, z}] (* A203696 *)

%K nonn

%O 1,2

%A _Clark Kimberling_, Jan 04 2012