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A340561
Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = sqrt( Product_{a=1..n-1} Product_{b=1..k-1} (4*sin(a*Pi/n)^2 + 4*cos(b*Pi/k)^2) ).
2
1, 1, 1, 1, 2, 1, 1, 5, 3, 1, 1, 12, 16, 4, 1, 1, 29, 75, 45, 5, 1, 1, 70, 361, 384, 121, 6, 1, 1, 169, 1728, 3509, 1805, 320, 7, 1, 1, 408, 8281, 31500, 30976, 8100, 841, 8, 1, 1, 985, 39675, 284089, 508805, 261725, 35287, 2205, 9, 1
OFFSET
1,5
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 2, 5, 12, 29, 70, ...
1, 3, 16, 75, 361, 1728, ...
1, 4, 45, 384, 3509, 31500, ...
1, 5, 121, 1805, 30976, 508805, ...
1, 6, 320, 8100, 261725, 7741440, ...
PROG
(PARI) default(realprecision, 120);
{T(n, k) = round(sqrt(prod(a=1, n-1, prod(b=1, k-1, 4*sin(a*Pi/n)^2+4*cos(b*Pi/k)^2))))}
CROSSREFS
Columns 1..4 give A000012, A000027, A004146, A006235.
Rows 1..3 give A000012, A000129, A005386.
Main diagonal gives A340563.
T(n, 2*n) gives A252767.
Sequence in context: A368487 A055818 A106240 * A097615 A288386 A062993
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jan 11 2021
STATUS
approved