|
|
A340396
|
|
a(n) = 2^(n^2 - 1) * Product_{j=1..n, k=1..n} (1 + sin(Pi*j/n)^2 + sin(Pi*k/n)^2).
|
|
2
|
|
|
0, 1, 96, 93789, 1244160000, 241885578271872, 700566272328037500000, 30323548995402141685610526683, 19627362048402730985830806120284160000, 189995156103157091521654945902925881881155376920, 27506190205802587152768139358989866456457087869970721213256
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 2^(n^2-1) * Product_{j=1..n, k=1..n} (3 - cos(Pi*j/n)^2 - cos(Pi*k/n)^2).
a(n) = 2^(n^2-1) * Product_{j=1..n, k=1..n} (2-cos(2*Pi*j/n)/2-cos(2*Pi*k/n)/2).
a(n) ~ 2^(n^2-1) * exp(4*c*n^2/Pi^2), where c = Integral_{x=0..Pi/2, y=0..Pi/2} (log(1 + sin(x)^2 + sin(y)^2) dy dx = -Pi^2*(log(2) + log(sqrt(2)-1)/2) + Pi * Integral_{x=0..Pi/2} log(1 + sqrt(1 + 1/(1 + sin(x)^2))) dx = A340421 = 1.627008991085721315763766677017604437985734719035793082916212355323520649...
|
|
MATHEMATICA
|
Table[2^(n^2 - 1) * Product[1 + Sin[Pi*j/n]^2 + Sin[Pi*k/n]^2, {j, 1, n}, {k, 1, n}], {n, 0, 10}] // Round
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|