A340428 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 * sin(b*Pi/(2*k+1))^2).

1, 1, 1, 1, 7, 1, 1, 61, 61, 1, 1, 547, 4961, 547, 1, 1, 4921, 432461, 432461, 4921, 1, 1, 44287, 38484961, 371647151, 38484961, 44287, 1, 1, 398581, 3445022461, 330435708793, 330435708793, 3445022461, 398581, 1

Offset

0,5

Links

Table of n, a(n) for n=0..35.

Formula

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

Example

Square array begins:
  1,    1,        1,            1,                1, ...
  1,    7,       61,          547,             4921, ...
  1,   61,     4961,       432461,         38484961, ...
  1,  547,   432461,    371647151,     330435708793, ...
  1, 4921, 38484961, 330435708793, 2952717950351617, ...

Prog

(PARI) 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))*sin(b*Pi/(2*k+1)))^2)))}

Crossrefs

Main diagonal gives A340292.

Cf. A340427, A340430, A340432.

Sequence in context: A174719 A176392 A015118 * A174691 A156692 A188644

Adjacent sequences: A340425 A340426 A340427 * A340429 A340430 A340431

Keyword

nonn,tabl

Author

Seiichi Manyama, Jan 07 2021

Status

approved