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A178451 Coefficients in series expansion of 1/j_inv, where j_inv (A091406) is the reversion of the j-function. 4
1, -744, -196884, -167975456, -180592706130, -217940004309744, -282054965806724344, -382591095354251539392, -536797252082856840544683, -772598111838972001258770120, -1134346327935015067651297762308, -1692324738742597705005194275401888, -2558136060792026773012451913035887538, -3909566534059719280565543662082528637552, -6030806348626044568366137322595811547663800, -9377648421379464305085605549750143357652168640, -14683413510495912973021347501907744913788055440950 (list; graph; refs; listen; history; text; internal format)
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 = -250.3989185574412282530281713739868122541444992745630952... - Vaclav Kotesovec, Jul 03 2017

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-Fran├žois 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 A091406

Adjacent sequences:  A178448 A178449 A178450 * A178452 A178453 A178454

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Dec 22 2010

STATUS

approved

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Last modified August 17 15:02 EDT 2017. Contains 290635 sequences.