A282045 Coefficients in solution to a certain functional equation.

1, 12, 168, 2496, 38328, 600672, 9539808, 152891520, 2466138552, 39966566304, 650017375488, 10601365433088, 173287953476448, 2837739346914432, 46542227947686912, 764357417859726336, 12567429586754388408, 206842036732301620896, 3407427981753822944448

Offset

0,2

Links

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

Shaun Cooper, Jesús Guillera, Armin Straub, Wadim Zudilin, Crouching AGM, Hidden Modularity, arXiv:1604.01106 [math.NT], 5-April-2016. See Section 2.

Formula

From Andrey Zabolotskiy, Feb 22 2017: (Start)

G.f. f(z) satisfies f(z/(1+mu*z)^3) / (1+mu*z)^2 = f(z^2/(1+lambda*z)^3) / (1+lambda*z)^2 with mu=2, lambda=-4.

a(n) = Sum_{0<=k<=n} A282046(k)*A282046(n-k), i.e., this is a convolution transform of A282046. Hence f(z)=g(z)^2, where g(z) is the g.f. of A282046.

(End)

Mathematica

terms=19; f[_]=1; Do[f[z_] = f[z]-f[z/(1+2z)^3] / (1+2z)^2+f[z^2/(1-4z)^3]/ (1-4z)^2 + O[z]^terms // Normal, {terms}]; f[z] // CoefficientList[#, z]& (* Jean-François Alcover, Oct 10 2018, after Andrey Zabolotskiy *)

Crossrefs

Cf. A282046.

Sequence in context: A079679 A216702 A320761 * A304960 A113380 A071103

Adjacent sequences: A282042 A282043 A282044 * A282046 A282047 A282048

Keyword

nonn

Author

N. J. A. Sloane, Feb 21 2017

Extensions

More terms from Andrey Zabolotskiy, Feb 22 2017

Status

approved