A340432 -id:A340432

Search: a340432 -id:a340432

Displaying 1-3 of 3 results found.

page 1

A340427

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

+10
4

1, 1, 1, 1, 12, 1, 1, 140, 140, 1, 1, 1632, 17745, 1632, 1, 1, 19024, 2227120, 2227120, 19024, 1, 1, 221760, 279215849, 2958176256, 279215849, 221760, 1, 1, 2585024, 35001302700, 3909096873216, 3909096873216, 35001302700, 2585024, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Table of n, a(n) for n=1..36.

FORMULA

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

T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - cos(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).

T(n,k) = 4^(2*(n-1)*(k-1)) * Product_{a=1..n-1} Product_{b=1..k-1} (1 - sin(a*Pi/(2*n))^2 * cos(b*Pi/(2*k))^2).

EXAMPLE

Square array begins:

1, 1, 1, 1, 1, ...

1, 12, 140, 1632, 19024, ...

1, 140, 17745, 2227120, 279215849, ...

1, 1632, 2227120, 2958176256, 3909096873216, ...

1, 19024, 279215849, 3909096873216, 54090331699622625, ...

PROG

(PARI) default(realprecision, 120);

{T(n, k) = round(4^(2*(n-1)*(k-1))*prod(a=1, n-1, prod(b=1, k-1, 1-(sin(a*Pi/(2*n))*sin(b*Pi/(2*k)))^2)))}

CROSSREFS

Main diagonal gives A340166.

Cf. A340425, A340428, A340430, A340432.

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jan 07 2021

STATUS

approved

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).

+10
3

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

(list; table; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jan 07 2021

STATUS

approved

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).

+10
3

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

(list; table; graph; refs; listen; history; text; internal format)

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.

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jan 07 2021

STATUS

approved

page 1

Search completed in 0.006 seconds