A178451 Coefficients in series expansion of 1/j_inv, where j_inv (A091406) is the reversion of the j-function.

1, -744, -196884, -167975456, -180592706130, -217940004309744, -282054965806724344, -382591095354251539392, -536797252082856840544683, -772598111838972001258770120, -1134346327935015067651297762308, -1692324738742597705005194275401888, -2558136060792026773012451913035887538, -3909566534059719280565543662082528637552, -6030806348626044568366137322595811547663800, -9377648421379464305085605549750143357652168640, -14683413510495912973021347501907744913788055440950

Offset

-1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = -1..300

Y.-H. He and V. Jejjala, Modular Matrix Models. See Eq. 72.

Formula

a(n) ~ c * 1728^n / n^(3/2), where c = -2 * exp(2*Pi) * Gamma(3/4)^4 / (sqrt(3) * Pi^(3/2)) = -250.3989185574412282530281713739868122541444992745630952... - Vaclav Kotesovec, Jul 03 2017, updated Mar 07 2018

Mathematica

nmax = 20; s1 = 1728*Series[KleinInvariantJ[t], {t, 0, 2*nmax}] /.t -> -2*I*(Pi/Log[q]); s2 = Normal[InverseSeries[Series[s1, {q, 0, nmax}], j]] /.j -> 1/x; CoefficientList[Series[x/s2, {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 03 2017 after Jean-François Alcover *)

Prog

(PARI)
x = 'x+O('x^50);
A=x*(eta(x^2)/eta(x))^24;
r=serreverse(A/(1+256*A)^3);
Vec( 1/r ) /* show terms */

Crossrefs

Cf. A000521, A091406, A066396.

Sequence in context: A288261 A000521 A178449 * A066395 A161557 A294182

Adjacent sequences: A178448 A178449 A178450 * A178452 A178453 A178454

Keyword

sign,easy

Author

N. J. A. Sloane, Dec 22 2010

Status

approved