The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A340432 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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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).
(history; published version)

#11 by Vaclav Kotesovec at Fri Jan 08 06:41:23 EST 2021

STATUS

proposed

approved

#10 by Seiichi Manyama at Fri Jan 08 06:38:26 EST 2021

STATUS

editing

proposed

#9 by Seiichi Manyama at Fri Jan 08 06:38:14 EST 2021

NAME

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

STATUS

approved

editing

#8 by N. J. A. Sloane at Thu Jan 07 10:35:01 EST 2021

STATUS

proposed

approved

#7 by Seiichi Manyama at Thu Jan 07 10:32:51 EST 2021

STATUS

editing

proposed

#6 by Seiichi Manyama at Thu Jan 07 10:25:50 EST 2021

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)))}

#5 by Seiichi Manyama at Thu Jan 07 10:21:51 EST 2021

CROSSREFS

Cf. A340427, A340428, A340430.

#4 by Seiichi Manyama at Thu Jan 07 10:19:10 EST 2021

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], ...

#3 by Seiichi Manyama at Thu Jan 07 10:17:11 EST 2021

EXAMPLE

[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]

CROSSREFS

Main diagonal gives A340295.

KEYWORD

nonn,changed,tabl

#2 by Seiichi Manyama at Thu Jan 07 10:16:21 EST 2021

NAME

allocated for Seiichi ManyamaSquare array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) = 4^(2*n*k) * Product_{1<=a<=n} Product_{1<=b<=k} (1 - sin(a*Pi/(2*n+1))^2 * cos(b*Pi/(2*k+1))^2).

DATA

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

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Jan 07 2021

STATUS

approved

editing