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A340560 Square array T(n,k), n >= 1, k >= 1, read by antidiagonals, where T(n,k) = Product_{a=1..n-1} Product_{b=1..k-1} (4*sin(a*Pi/n)^2 + 4*sin(b*Pi/k)^2). 3
1, 1, 1, 1, 8, 1, 1, 49, 49, 1, 1, 288, 1296, 288, 1, 1, 1681, 30625, 30625, 1681, 1, 1, 9800, 707281, 2654208, 707281, 9800, 1, 1, 57121, 16257024, 219069601, 219069601, 16257024, 57121, 1, 1, 332928, 373301041, 17860500000, 62500000000, 17860500000, 373301041, 332928, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
LINKS
FORMULA
T(n,k) = T(k,n).
T(n,k) = A212796(n,k)/(n*k).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, ...
1, 8, 49, 288, 1681, ...
1, 49, 1296, 30625, 707281, ...
1, 288, 30625, 2654208, 219069601, ...
1, 1681, 707281, 219069601, 62500000000, ...
PROG
(PARI) default(realprecision, 120);
{T(n, k) = round(prod(a=1, n-1, prod(b=1, k-1, 4*sin(a*Pi/n)^2+4*sin(b*Pi/k)^2)))}
CROSSREFS
Rows and columns 1..2 give A000012, A001108.
Main diagonal gives A340562.
Sequence in context: A174528 A259465 A176227 * A022171 A203443 A176642
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Jan 11 2021
STATUS
approved

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Last modified February 26 10:17 EST 2024. Contains 370342 sequences. (Running on oeis4.)