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13, 1519, 490827, 310285521, 323965491213, 505036803636351, 1099306007175141675, 3185114376029382371169, 11851908573273735083748813, 55083172732097477388836049999, 312715835695576039538837531922507
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OFFSET
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1,1
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COMMENTS
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See A093883 for a discussion and guide to related sequences.
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LINKS
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FORMULA
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a(n) = (1/(2^n * n!))*Product_{j=1..n} ((2*n+1)^3 - (2*j-1)^3). - G. C. Greubel, Feb 23 2024
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MATHEMATICA
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(* First program *)
f[j_]:= 2 j - 1; z = 12;
v[n_]:= Product[f[j]^2 + f[j]*f[k] + f[k]^2, {k, 2, n}, {j, k-1}]
Table[v[n + 1]/v[n], {n, z}] (* A203515 *)
(* Second program *)
A203515[n_]:= Product[(2*n+1)^3 - (2*j-1)^3, {j, n}]/(2^n*n!);
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PROG
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(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
(SageMath)
def A203515(n): return product((2*n+1)^3 -(2*j-1)^3 for j in range(1, n+1))/(2^n*factorial(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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