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)))}
A340295
a(n) = 4^(2*n^2) * Product_{1<=j,k<=n} (1 - sin(j*Pi/(2*n+1))^2 * cos(k*Pi/(2*n+1))^2).
Original entry on oeis.org
1, 13, 18281, 2732887529, 43384923739812577, 73125714588602035608260981, 13085551252412040683513520733767180041, 248596840858215958581954513797323868183183928594833
Offset: 0
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Table[Resultant[ChebyshevT[4*n+2, x/2], ChebyshevT[4*n+2, I*x/2], x]^(1/4) / 2^n, {n, 0, 10}] (* 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))*cos(k*Pi/(2*n+1)))^2)))}
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{a(n) = sqrtint(sqrtint(polresultant(polchebyshev(4*n+2, 1, x/2), polchebyshev(4*n+2, 1, I*x/2))))/2^n}
A340428
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 * sin(b*Pi/(2*k+1))^2).
Original entry on oeis.org
1, 1, 1, 1, 7, 1, 1, 61, 61, 1, 1, 547, 4961, 547, 1, 1, 4921, 432461, 432461, 4921, 1, 1, 44287, 38484961, 371647151, 38484961, 44287, 1, 1, 398581, 3445022461, 330435708793, 330435708793, 3445022461, 398581, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, ...
1, 7, 61, 547, 4921, ...
1, 61, 4961, 432461, 38484961, ...
1, 547, 432461, 371647151, 330435708793, ...
1, 4921, 38484961, 330435708793, 2952717950351617, ...
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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))*sin(b*Pi/(2*k+1)))^2)))}
A340293
a(n) = 4^((n-1)*n) * Product_{1<=j
Original entry on oeis.org
1, 1, 11, 1247, 1455913, 17511093953, 2169916151129091, 2770393222231417622719, 36443188794328204864735075793, 4939371777650229260975457785579794433, 6897784079863728378183626237683602071537213179
Offset: 0
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Table[2^(2*n*(n-1)) * Product[Product[1 - Sin[j*Pi/(2*n + 1)]^2*Sin[k*Pi/(2*n + 1)]^2, {k, j+1, n}], {j, 1, n}], {n, 0, 12}] // Round (* Vaclav Kotesovec, Jan 04 2021 *)
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default(realprecision, 120);
{a(n) = round(4^((n-1)*n)*prod(j=1, n, prod(k=j+1, n, 1-(sin(j*Pi/(2*n+1))*sin(k*Pi/(2*n+1)))^2)))}
Showing 1-4 of 4 results.
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