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A288846 Expansion of (q*j)^3, where j is a modular function A000521. 6

%I

%S 1,2232,2251260,1355202240,541778118390,151522053809760,

%T 30456116651640888,4460775211418664960,479919718908048515625,

%U 38292247221915373896560,2309356967925215526546564,108570959012192293978767360,4111854826236389868361040550

%N Expansion of (q*j)^3, where j is a modular function A000521.

%H Vaclav Kotesovec, <a href="/A288846/b288846.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)

%F G.f.: ((1 + 240 Sum_{k>0} k^3 q^k/(1-q^k))^3/(Product_{k>0} (1-q^k)^24))^3.

%F a(n) ~ 3^(1/4) * exp(4*Pi*sqrt(3*n)) / (sqrt(2)*n^(3/4)). - _Vaclav Kotesovec_, Jun 29 2017

%t CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^9, {x, 0, 20}], x] (* _Vaclav Kotesovec_, Jun 29 2017 *)

%t (q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^3 + O[q]^13 // CoefficientList[#, q]& (* _Jean-Fran├žois Alcover_, Nov 02 2017 *)

%Y Cf. A000521 (j(q)), A004009 (E_4), A008411 (E_4^3).

%Y (q*j(q))^(k/24): A289397 (k=-1), A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), A289300 (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12), A028512 (k=16), A028513 (k=32), A028514 (k=40), A028515 (k=48), this sequence (k=72).

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jun 18 2017

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Last modified May 22 18:53 EDT 2019. Contains 323481 sequences. (Running on oeis4.)