A299830 Coefficients in expansion of (q*j(q))^(-1/4) where j(q) is the elliptic modular invariant (A000521).

1, -186, 37269, -7859330, 1697901090, -371924784000, 82208011242071, -18286478726628018, 4086893434159800000, -916721490080116189690, 206224024157150867919738, -46501365201275569893140034, 10506135153567544547655979849

Offset

0,2

Links

Table of n, a(n) for n=0..12.

Formula

Convolution inverse of A289301.

a(n) ~ (-1)^n * c * exp(Pi*sqrt(3)*n) / n^(1/4), where c = 0.863092410616421890391706584312871736447175709008670875907... = 2^(1/4) * exp(sqrt(3) * Pi/4) * Pi^2 * Gamma(1/4) / (3^(3/4) * Gamma(1/3)^(9/2)). - Vaclav Kotesovec, Feb 20 2018, updated Mar 06 2018

a(n) * A289301(n) ~ -3*exp(2*sqrt(3)*Pi*n) / (2^(5/2)*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018

Mathematica

CoefficientList[Series[(2 * QPochhammer[-1, x])^6 / (65536 + x*QPochhammer[-1, x]^24)^(3/4), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 20 2018 *)

Crossrefs

Cf. A000521, A289301.

Sequence in context: A161619 A206515 A366488 * A265171 A146502 A231055

Adjacent sequences: A299827 A299828 A299829 * A299831 A299832 A299833

Keyword

sign

Author

Seiichi Manyama, Feb 20 2018

Status

approved