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 A289300 Expansion of (q*j(q))^(5/24) where j(q) is the elliptic modular invariant (A000521). 18
 1, 155, -4630, 601265, -83644610, 13148835656, -2223584717035, 395257299676190, -72843145114522035, 13796578308407774725, -2669652272250261922223, 525556527400692937755655, -104937908072571416700653120 (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)^(5*A192731(n)/24). a(n) ~ (-1)^(n+1) * c * exp(Pi*sqrt(3)*n) / n^(13/8), where c = 0.251632947646443757912747944865268710111059274679945447776728146817... = 5 * 3^(5/8) * sqrt(2 + sqrt(2)) * Gamma(1/3)^(15/4) * Gamma(5/8) / (2^(37/8) * exp(5 * Pi / (8 * sqrt(3))) * Pi^(7/2)). - Vaclav Kotesovec, Jul 03 2017, updated Mar 06 2018 a(n) * A299829(n) ~ -5*sqrt(2 + sqrt(2)) * exp(2*sqrt(3)*Pi*n) / (16*Pi*n^2). - Vaclav Kotesovec, Feb 20 2018 MATHEMATICA CoefficientList[Series[(65536 + x*QPochhammer[-1, x]^24)^(5/8) / (2*QPochhammer[-1, x])^5, {x, 0, 20}], x] (* Vaclav Kotesovec, Sep 23 2017 *) (q*1728*KleinInvariantJ[-Log[q]*I/(2*Pi)])^(5/24) + O[q]^13 // CoefficientList[#, q]& (* Jean-François Alcover, Nov 02 2017 *) CROSSREFS (q*j(q))^(k/24): A106205 (k=1), A289297 (k=2), A289298 (k=3), A289299 (k=4), this sequence (k=5), A289301 (k=6), A289302 (k=7), A007245 (k=8), A289303 (k=9), A289304 (k=10), A289305 (k=11), A161361 (k=12). Cf. A000521, A192731. Sequence in context: A010086 A110834 A110842 * A220592 A278730 A278432 Adjacent sequences:  A289297 A289298 A289299 * A289301 A289302 A289303 KEYWORD sign AUTHOR Seiichi Manyama, Jul 02 2017 STATUS approved

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Last modified May 19 06:38 EDT 2019. Contains 323386 sequences. (Running on oeis4.)