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%I #12 Feb 23 2024 01:47:12
%S 13,1519,490827,310285521,323965491213,505036803636351,
%T 1099306007175141675,3185114376029382371169,
%U 11851908573273735083748813,55083172732097477388836049999,312715835695576039538837531922507
%N a(n) = A203514(n+1)/A203514(n).
%C See A093883 for a discussion and guide to related sequences.
%H G. C. Greubel, <a href="/A203515/b203515.txt">Table of n, a(n) for n = 1..185</a>
%F a(n) = (1/(2^n * n!))*Product_{j=1..n} ((2*n+1)^3 - (2*j-1)^3). - _G. C. Greubel_, Feb 23 2024
%t (* First program *)
%t f[j_]:= 2 j - 1; z = 12;
%t v[n_]:= Product[f[j]^2 + f[j]*f[k] + f[k]^2, {k,2,n}, {j,k-1}]
%t Table[v[n], {n, z}] (* A203514 *)
%t Table[v[n + 1]/v[n], {n, z}] (* A203515 *)
%t (* Second program *)
%t A203515[n_]:= Product[(2*n+1)^3 - (2*j-1)^3, {j,n}]/(2^n*n!);
%t Table[A203515[n], {n,30}] (* _G. C. Greubel_, Feb 23 2024 *)
%o (Magma) [(&*[(2*n+1)^3 -(2*j-1)^3: j in [1..n]])/(2^n*Factorial(n)): n in [1..30]]; // _G. C. Greubel_, Feb 23 2024
%o (SageMath)
%o def A203515(n): return product((2*n+1)^3 -(2*j-1)^3 for j in range(1, n+1))/(2^n*factorial(n))
%o [A203515(n) for n in range(1,31)] # _G. C. Greubel_, Feb 23 2024
%Y Cf. A093883, A203514.
%K nonn
%O 1,1
%A _Clark Kimberling_, Jan 04 2012
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