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A289302 Expansion of (q*j(q))^(7/24) where j(q) is the elliptic modular invariant (A000521). 17
1, 217, 245, 231350, -27293420, 4017072017, -643057897118, 109259930443485, -19377905432572925, 3549922504344871655, -666990037937425724641, 127890778891452935279096, -24934077008209243436961385 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..425

FORMULA

G.f.: Product_{n>=1} (1-q^n)^(7*A192731(n)/24).

a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(15/8), where c = 0.108789720644871714449969800661839212719879897088563371823367481878... = 7 * 3^(7/8) * sqrt(2 - sqrt(2)) * Gamma(1/3)^(21/4) * Gamma(7/8) / (2^(39/8) * exp(7 * Pi / (8 * sqrt(3))) * Pi^(9/2)). - Vaclav Kotesovec, Jul 03 2017, updated Mar 06 2018

MATHEMATICA

CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^(7/8) / (2*QPochhammer[-1, x])^7, {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 23 2017 *)

(q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^(7/24) + O[q]^13 // CoefficientList[#, q]& (* Jean-Fran├žois Alcover, Nov 02 2017 *)

CROSSREFS

(q*j(q))^(k/24): A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), this sequence (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12).

Cf. A000521, A192731.

Sequence in context: A038661 A044877 A204765 * A288847 A102658 A145732

Adjacent sequences:  A289299 A289300 A289301 * A289303 A289304 A289305

KEYWORD

sign

AUTHOR

Seiichi Manyama, Jul 02 2017

STATUS

approved

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Last modified May 21 03:19 EDT 2019. Contains 323434 sequences. (Running on oeis4.)