A340432 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 * cos(b*Pi/(2*k+1))^2).

1, 1, 1, 1, 13, 1, 1, 121, 181, 1, 1, 1093, 18281, 2521, 1, 1, 9841, 1690781, 2803921, 35113, 1, 1, 88573, 152963281, 2732887529, 430503601, 489061, 1, 1, 797161, 13755675781, 2555011015201, 4447515497881, 66102491401, 6811741, 1

Offset

0,5

Links

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

Example

Square array begins:
  1,     1,         1,             1,                 1, ...
  1,    13,       121,          1093,              9841, ...
  1,   181,     18281,       1690781,         152963281, ...
  1,  2521,   2803921,    2732887529,     2555011015201, ...
  1, 35113, 430503601, 4447515497881, 43384923739812577, ...

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

Crossrefs

Main diagonal gives A340295.

Cf. A340427, A340428, A340430.

Sequence in context: A342891 A174694 A353952 * A156539 A172300 A022176

Adjacent sequences: A340429 A340430 A340431 * A340433 A340434 A340435

Keyword

nonn,tabl

Author

Seiichi Manyama, Jan 07 2021

Status

approved