A340475 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = Product_{a=1..n} Product_{b=1..k} (4*sin(a*Pi/(2*n+1))^2 + 4*sin(b*Pi/(2*k+1))^2).

1, 1, 1, 1, 6, 1, 1, 29, 29, 1, 1, 139, 500, 139, 1, 1, 666, 8329, 8329, 666, 1, 1, 3191, 138301, 463736, 138301, 3191, 1, 1, 15289, 2295701, 25543057, 25543057, 2295701, 15289, 1, 1, 73254, 38105729, 1404312491, 4614756624, 1404312491, 38105729, 73254, 1

Offset

0,5

Links

Table of n, a(n) for n=0..44.

Formula

T(n,k) = T(k,n).

Example

Square array begins:
  1,   1,      1,        1,          1, ...
  1,   6,     29,      139,        666, ...
  1,  29,    500,     8329,     138301, ...
  1, 139,   8329,   463736,   25543057, ...
  1, 666, 138301, 25543057, 4614756624, ...

Prog

(PARI) default(realprecision, 120);
{T(n, k) = round(prod(a=1, n, prod(b=1, k, 4*sin(a*Pi/(2*n+1))^2+4*sin(b*Pi/(2*k+1))^2)))}

Crossrefs

Rows and columns 0..1 give A000012, A030221.

Main diagonal gives A127605.

Cf. A116469, A187617, A340476.

Sequence in context: A105373 A296548 A201461 * A368848 A265603 A174186

Adjacent sequences: A340472 A340473 A340474 * A340476 A340477 A340478

Keyword

nonn,tabl

Author

Seiichi Manyama, Jan 09 2021

Status

approved