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1, 3, 84, 273000, 3046699656000, 5996663814749677445376000, 160771799453017261771769947549079938007040000, 6351968589735888467306807912855132014808202373395298410963148996608000000
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OFFSET
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1,2
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COMMENTS
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It is conjectured that every term of the sequence is an integer.
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LINKS
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FORMULA
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a(n) ~ c * A * n^(n^3/3 - n^2/4 - 7*n/12 + 17/24) * (2*Pi)^(n^2/4 - 3*n/4) / exp(4*n^3/9 - 7*n^2/8 - n + 1/12), where A is the Glaisher-Kinkelin constant A074962 and c = 0.488888619502150098591650327163991582267254151817880403495924251381414248582... (from A203482). - Vaclav Kotesovec, Nov 20 2023
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MATHEMATICA
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f[j_] := j!; z = 10;
v[n_] := Product[Product[f[k] + f[j], {j, 1, k - 1}], {k, 2, n}]
d[n_] := Product[(i - 1)!, {i, 1, n}] (* A000178 *)
Table[v[n], {n, 1, z}] (* A203482 *)
Table[v[n + 1]/v[n], {n, 1, z - 1}] (* A203483 *)
Table[v[n]/d[n], {n, 1, 10}] (* this sequence *)
Table[Product[j! + k!, {j, 1, n}, {k, 1, j-1}] / BarnesG[n+1], {n, 1, 10}] (* Vaclav Kotesovec, Nov 20 2023 *)
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PROG
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(Magma)
BarnesG:= func< n | (&*[Factorial(k): k in [0..n-2]]) >;
A203510:= func< n | n eq 1 select 1 else (&*[(&*[Factorial(j) + Factorial(k): k in [1..j-1]]): j in [2..n]])/BarnesG(n+1) >;
(SageMath)
def BarnesG(n): return product(factorial(j) for j in range(1, n-1))
def A203510(n): return product(product(factorial(j)+factorial(k) for k in range(1, j)) for j in range(1, n+1))/BarnesG(n+1)
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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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