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 A203510 a(n) = A203482(n) / A000178(n). 3
 1, 3, 84, 273000, 3046699656000, 5996663814749677445376000, 160771799453017261771769947549079938007040000, 6351968589735888467306807912855132014808202373395298410963148996608000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS It is conjectured that every term of the sequence is an integer. LINKS G. C. Greubel, Table of n, a(n) for n = 1..16 FORMULA 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 MATHEMATICA 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 *) PROG (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) >; [A203510(n): n in [1..13]]; // G. C. Greubel, Feb 24 2024 (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) [A203510(n) for n in range(1, 14)] # G. C. Greubel, Feb 24 2024 CROSSREFS Cf. A000142, A000178, A074962, A093883, A203482, A203483. Sequence in context: A179431 A116303 A215911 * A065162 A056262 A042587 Adjacent sequences: A203507 A203508 A203509 * A203511 A203512 A203513 KEYWORD nonn,changed AUTHOR Clark Kimberling, Jan 03 2012 STATUS approved

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Last modified March 2 17:21 EST 2024. Contains 370497 sequences. (Running on oeis4.)