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 A340166 a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 - sin(i*Pi/(2*n))^2 * sin(j*Pi/(2*n))^2). 10
 1, 12, 17745, 2958176256, 54090331699622625, 107181043200192494332800000, 22868509031094388112997259982567521313, 523389340935243821042846225254323436248483571433472 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..30 D. E. Knuth, Aztec Diamonds, Checkerboard Graphs, and Spanning Trees, arXiv:math/9501234 [math.CO], 1995; J. Alg. Combinatorics 6 (1997), 253-257. FORMULA a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 - cos(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2). a(n) = 4^(2*(n-1)^2) * Product_{1<=i,j<=n-1} (1 - sin(i*Pi/(2*n))^2 * cos(j*Pi/(2*n))^2). a(n) ~ Gamma(1/4) * exp(8*G*n^2/Pi) / (Pi^(3/4) * sqrt(n) * 2^(6*n - 2)), where G is Catalan's constant A006752. - Vaclav Kotesovec, Jan 05 2021 MATHEMATICA Table[4^(2*(n-1)^2) * Product[Product[1 - Sin[i*Pi/(2*n)]^2 * Sin[j*Pi/(2*n)]^2, {i, 1, n-1}], {j, 1, n-1}], {n, 1, 10}] // Round (* Vaclav Kotesovec, Dec 31 2020 *) PROG (PARI) default(realprecision, 120); {a(n) = round(4^(2*(n-1)^2)*prod(i=1, n-1, prod(j=1, n-1, 1-(sin(i*Pi/(2*n))*sin(j*Pi/(2*n)))^2)))} CROSSREFS Cf. A007725, A340139, A340167. Sequence in context: A012674 A301533 A013514 * A125547 A159421 A159369 Adjacent sequences: A340163 A340164 A340165 * A340167 A340168 A340169 KEYWORD nonn AUTHOR Seiichi Manyama, Dec 30 2020 STATUS approved

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Last modified July 24 11:31 EDT 2024. Contains 374583 sequences. (Running on oeis4.)