A320519 a(n) = 2*n^n*cos(n*arcsin(sqrt(4*n^2-1)/(2*n))) for n > 0 and a(0) = 2.

2, 1, -7, -26, 449, 3001, -81863, -790271, 29441537, 371653678, -17549650999, -273657699479, 15647990550337, 290477695697281, -19502273553366631, -419946226750915874, 32375641678132277249, 793304922112119056161, -69057016330377072921047, -1897210272812469982747199

Offset

0,1

Links

Table of n, a(n) for n=0..19.

Formula

For n > 0, a(n) = n^n*(h(n)^(-n) + h(n)^n) where h(n) = (1 + i*sqrt(4*n^2 - 1))/(2*n).

For n > 0, a(n) = 2 * n^n * cos(n*arctan(sqrt(4*n^2 - 1))). - Vladimir Reshetnikov, Oct 14 2018

Crossrefs

Cf. A320534.

Sequence in context: A141516 A235378 A214327 * A183272 A138346 A085073

Adjacent sequences: A320516 A320517 A320518 * A320520 A320521 A320522

Keyword

sign

Author

Peter Luschny, Oct 14 2018

Status

approved