A059944 Denominators of Maclaurin series coefficients for 2*cos(x/sqrt(3) + arctan(-sqrt(3))) = cos(x/sqrt(3)) + sqrt(3)*sin(x/sqrt(3)).

1, 1, 6, 18, 216, 1080, 19440, 136080, 3265920, 29393280, 881798400, 9699782400, 349192166400, 4539498163200, 190658922854400, 2859883842816000, 137274424455168000, 2333665215737856000, 126017921649844224000

Offset

0,3

Comments

Related to the exact solution of the logistic equation with r = -2.

Denominators of Maclaurin series coefficients of (sqrt(n) + 1)/2*exp(x/sqrt(n)) - (sqrt(n) - 1)/2*exp(-x/sqrt(n)) = 1 + x + x^2/(n*2!) + x^3/(n*3!) + x^4/(n^2*4!) + x^5/(n^2*5!) + ... when n = 3. Cf. A268363 (case n = 2). - Peter Bala, Aug 06 2019

Links

Table of n, a(n) for n=0..18.

Eric Weisstein's World of Mathematics, Logistic Equation.

Formula

a(n) = 3^floor(n/2)*n! = Product_{k = 1..n} k*(2 - (-1)^(k-1)) = Product_{k = 0..n-1} A165998(k), with empty products set equal to 1. - Peter Bala, Aug 05 2019

a(n) = denominator([x^n] 2*sin(x/sqrt(3) + Pi/6)). Numerator is A057077. - Peter Luschny, Aug 07 2019

Maple

gf := 2*sin(x/sqrt(3) + Pi/6): ser := series(gf, x, 20):
seq(denom(coeff(ser, x, n)), n=0..18); # Peter Luschny, Aug 07 2019

Crossrefs

Cf. A165998, A268363, A057077.

Sequence in context: A077531 A214537 A052634 * A052139 A354019 A052682

Adjacent sequences: A059941 A059942 A059943 * A059945 A059946 A059947

Keyword

nonn,easy

Author

Eric W. Weisstein

Status

approved