A340430 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 - cos(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).

1, 1, 1, 1, 15, 1, 1, 209, 209, 1, 1, 2911, 32625, 2911, 1, 1, 40545, 5015009, 5015009, 40545, 1, 1, 564719, 770100001, 8238791743, 770100001, 564719, 1, 1, 7865521, 118247646001, 13441754883649, 13441754883649, 118247646001, 7865521, 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,    15,       209,           2911,              40545, ...
  1,   209,     32625,        5015009,          770100001, ...
  1,  2911,   5015009,     8238791743,     13441754883649, ...
  1, 40545, 770100001, 13441754883649, 230629380093001665, ...

Prog

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

Crossrefs

Main diagonal gives A340291.

Cf. A340427, A340428, A340432.

Sequence in context: A156939 A174187 A174693 * A022178 A176639 A015139

Adjacent sequences: A340427 A340428 A340429 * A340431 A340432 A340433

Keyword

nonn,tabl

Author

Seiichi Manyama, Jan 07 2021

Status

approved