A340291
a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - cos(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).
Original entry on oeis.org
1, 15, 32625, 8238791743, 230629380093001665, 703130165949449759361247759, 231459008314298532714943209968328640625, 8186710889725936196671113787217620194601044287109375
Offset: 0
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Table[2^(4*n^2) * Product[Product[1 - Cos[j*Pi/(2*n+1)]^2 * Cos[k*Pi/(2*n+1)]^2, {j, 1, n}], {k, 1, n}], {n, 0, 10}] // Round (* Vaclav Kotesovec, Jan 03 2021 *)
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default(realprecision, 120);
{a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(cos(j*Pi/(2*n+1))*cos(k*Pi/(2*n+1)))^2)))}
A340292
a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - sin(j*Pi/(2*n+1))^2 * sin(k*Pi/(2*n+1))^2).
Original entry on oeis.org
1, 7, 4961, 371647151, 2952717950351617, 2489597262406609716450871, 222812636926792555435326125877303201, 2116840405025957772469476908228785308996001314527, 2134958300495920487325052422663717579194357002081033470045923329
Offset: 0
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Table[2^(4*n^2) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2 * Sin[k*Pi/(2*n + 1)]^2, {k, 1, n}], {j, 1, n}], {n, 0, 10}] // Round (* Vaclav Kotesovec, Jan 04 2021 *)
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default(realprecision, 120);
{a(n) = round(4^(2*n^2)*prod(j=1, n, prod(k=1, n, 1-(sin(j*Pi/(2*n+1))*sin(k*Pi/(2*n+1)))^2)))}
Original entry on oeis.org
1, 2, 13, 272, 18281, 3944920, 2732887529, 6077512159232, 43384923739812577, 994156445200670735008, 73125714588602035608260981, 17265651822746410593596262486016, 13085551252412040683513520733767180041, 31834381760532514451976501491991780699626368
Offset: 1
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Table[Resultant[ChebyshevT[2*n, x/2], ChebyshevT[2*n, I*x/2], x]^(1/4) / 2^((n-1)/2), {n, 1, 15}] (* Vaclav Kotesovec, Apr 14 2020 *)
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{a(n) = sqrtint(sqrtint(polresultant(polchebyshev(2*n, 1, x/2), polchebyshev(2*n, 1, I*x/2)))/2^(n-1))}
A340432
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{a=1..n} Product_{b=1..k} (1 - sin(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).
Original entry on oeis.org
1, 1, 1, 1, 13, 1, 1, 121, 181, 1, 1, 1093, 18281, 2521, 1, 1, 9841, 1690781, 2803921, 35113, 1, 1, 88573, 152963281, 2732887529, 430503601, 489061, 1, 1, 797161, 13755675781, 2555011015201, 4447515497881, 66102491401, 6811741, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, ...
1, 13, 121, 1093, 9841, ...
1, 181, 18281, 1690781, 152963281, ...
1, 2521, 2803921, 2732887529, 2555011015201, ...
1, 35113, 430503601, 4447515497881, 43384923739812577, ...
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default(realprecision, 120);
{T(n, k) = round(4^(2*n*k)*prod(a=1, n, prod(b=1, k, 1-(sin(a*Pi/(2*n+1))*cos(b*Pi/(2*k+1)))^2)))}
Showing 1-4 of 4 results.