This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A059944 #15 Feb 16 2025 08:32:44
%S A059944 1,1,6,18,216,1080,19440,136080,3265920,29393280,881798400,9699782400,
%T A059944 349192166400,4539498163200,190658922854400,2859883842816000,
%U A059944 137274424455168000,2333665215737856000,126017921649844224000
%N 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)).
%C A059944 Related to the exact solution of the logistic equation with r = -2.
%C A059944 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
%H A059944 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LogisticEquation.html">Logistic Equation.</a>
%F A059944 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
%F A059944 a(n) = denominator([x^n] 2*sin(x/sqrt(3) + Pi/6)). Numerator is A057077. - _Peter Luschny_, Aug 07 2019
%p A059944 gf := 2*sin(x/sqrt(3) + Pi/6): ser := series(gf, x, 20):
%p A059944 seq(denom(coeff(ser, x, n)), n=0..18); # _Peter Luschny_, Aug 07 2019
%Y A059944 Cf. A165998, A268363, A057077.
%K A059944 nonn,easy
%O A059944 0,3
%A A059944 _Eric W. Weisstein_