A299832 Coefficients in expansion of (q*j(q))^(-1/2) where j(q) is the elliptic modular invariant (A000521).

1, -372, 109134, -29582728, 7708451301, -1961287513020, 491099261627462, -121565597132437848, 29833005033279338994, -7271987659286598049924, 1763026435863342757734816, -425536800137353949416343064, 102330765938465480149314691831

Offset: 0

Author

Seiichi Manyama, Feb 20 2018

Keywords

• sign

Crossrefs

Cf. A000521, A161361.

Programs

Mathematica

CoefficientList[Series[(2 * QPochhammer[-1, x])^12 / (65536 + x*QPochhammer[-1, x]^24)^(3/2), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 20 2018 *)

Formula

Convolution inverse of A161361.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) * sqrt(n), where c = 1.26222636056850175307711547840462898041775779303411175244... = 2^(5/2) * exp(sqrt(3) * Pi/2) * Pi^(11/2) / (3^(3/2) * Gamma(1/3)^9). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018

a(n) * A161361(n) ~ 3*exp(2*sqrt(3)*Pi*n) / (2*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018