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A299830 Coefficients in expansion of (q*j(q))^(-1/4) where j(q) is the elliptic modular invariant (A000521). 3
1, -186, 37269, -7859330, 1697901090, -371924784000, 82208011242071, -18286478726628018, 4086893434159800000, -916721490080116189690, 206224024157150867919738, -46501365201275569893140034, 10506135153567544547655979849 (list; graph; refs; listen; history; text; internal format)
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: A241942 A161619 A206515 * A265171 A146502 A231055

Adjacent sequences:  A299827 A299828 A299829 * A299831 A299832 A299833

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 20 2018

STATUS

approved

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Last modified July 16 04:26 EDT 2019. Contains 325064 sequences. (Running on oeis4.)