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A127605 a(n) = 2^(2*n*n) * Product_{i=1..n} Product_{j=1..n} (sin(i*Pi/(2*n+1))^2 + sin(j*Pi/(2*n+1))^2). 7
1, 6, 500, 463736, 4614756624, 485005220494432, 533978739649683515200, 6129678550595328659594928000, 731483813983605533022316212534132992, 905665520470954445892575061753881157482726912 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) ~ Gamma(1/4) * exp(G*(2*n+1)^2/Pi) / (2^(3/2) * Pi^(3/4) * sqrt(n)), where G is Catalan's constant A006752. - Vaclav Kotesovec, Dec 30 2020
MAPLE
for n from 0 to 12 do a[n]:=2^(2*n*n)*product(product(sin(i*Pi/(2*n+1))^2+ sin(j*Pi/(2*n+1))^2, j=1..n), i=1..n) od: seq(round(evalf(a[n], 300)), n=0..12);
MATHEMATICA
Table[(2*n+1) * 2^(n*(2*n-1)) * Product[Product[Sin[i*Pi/(2*n + 1)]^2 + Sin[j*Pi/(2*n + 1)]^2, {i, 1, j-1}], {j, 2, n}]^2, {n, 0, 15}] // Round (* Vaclav Kotesovec, Dec 30 2020 *)
CROSSREFS
Sequence in context: A197803 A099057 A123278 * A278775 A013975 A272094
KEYWORD
nonn
AUTHOR
Miklos Kristof, Apr 03 2007
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)