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 A288846 Expansion of (q*j)^3, where j is a modular function A000521. 6
 1, 2232, 2251260, 1355202240, 541778118390, 151522053809760, 30456116651640888, 4460775211418664960, 479919718908048515625, 38292247221915373896560, 2309356967925215526546564, 108570959012192293978767360, 4111854826236389868361040550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..1000 from Seiichi Manyama) FORMULA G.f.: ((1 + 240 Sum_{k>0} k^3 q^k/(1-q^k))^3/(Product_{k>0} (1-q^k)^24))^3. a(n) ~ 3^(1/4) * exp(4*Pi*sqrt(3*n)) / (sqrt(2)*n^(3/4)). - Vaclav Kotesovec, Jun 29 2017 MATHEMATICA CoefficientList[Series[(QPochhammer[x, x^2]^8 + 256*x/QPochhammer[x, x^2]^16)^9, {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 29 2017 *) (q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^3 + O[q]^13 // CoefficientList[#, q]& (* Jean-François Alcover, Nov 02 2017 *) CROSSREFS Cf. A000521 (j(q)), A004009 (E_4), A008411 (E_4^3). (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). Sequence in context: A205981 A205038 A279661 * A289454 A079013 A186865 Adjacent sequences:  A288843 A288844 A288845 * A288847 A288848 A288849 KEYWORD nonn AUTHOR Seiichi Manyama, Jun 18 2017 STATUS approved

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Last modified April 21 04:56 EDT 2019. Contains 322310 sequences. (Running on oeis4.)