A340427
Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - sin(a*Pi/(2*n))^2 * sin(b*Pi/(2*k))^2).
Original entry on oeis.org
1, 1, 1, 1, 12, 1, 1, 140, 140, 1, 1, 1632, 17745, 1632, 1, 1, 19024, 2227120, 2227120, 19024, 1, 1, 221760, 279215849, 2958176256, 279215849, 221760, 1, 1, 2585024, 35001302700, 3909096873216, 3909096873216, 35001302700, 2585024, 1
Offset: 1
Square array begins:
1, 1, 1, 1, 1, ...
1, 12, 140, 1632, 19024, ...
1, 140, 17745, 2227120, 279215849, ...
1, 1632, 2227120, 2958176256, 3909096873216, ...
1, 19024, 279215849, 3909096873216, 54090331699622625, ...
-
default(realprecision, 120);
{T(n, k) = round(4^(2*(n-1)*(k-1))*prod(a=1, n-1, prod(b=1, k-1, 1-(sin(a*Pi/(2*n))*sin(b*Pi/(2*k)))^2)))}
A340430
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 - cos(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).
Original entry on oeis.org
1, 1, 1, 1, 15, 1, 1, 209, 209, 1, 1, 2911, 32625, 2911, 1, 1, 40545, 5015009, 5015009, 40545, 1, 1, 564719, 770100001, 8238791743, 770100001, 564719, 1, 1, 7865521, 118247646001, 13441754883649, 13441754883649, 118247646001, 7865521, 1
Offset: 0
Square array begins:
1, 1, 1, 1, 1, ...
1, 15, 209, 2911, 40545, ...
1, 209, 32625, 5015009, 770100001, ...
1, 2911, 5015009, 8238791743, 13441754883649, ...
1, 40545, 770100001, 13441754883649, 230629380093001665, ...
-
default(realprecision, 120);
{T(n, k) = round(4^(2*n*k)*prod(a=1, n, prod(b=1, k, 1-(cos(a*Pi/(2*n+1))*cos(b*Pi/(2*k+1)))^2)))}
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, ...
-
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 1-3 of 3 results.