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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).
4
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
1,5
FORMULA
T(n,k) = T(k,n).
T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - cos(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).
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 * cos(b*Pi/(2*k))^2).
EXAMPLE
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, ...
PROG
(PARI) 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)))}
CROSSREFS
Main diagonal gives A340166.
Sequence in context: A156280 A166962 A022175 * A176627 A015129 A172376
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jan 07 2021
STATUS
approved