# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a289563 Showing 1-1 of 1 %I A289563 #16 Mar 07 2018 17:11:17 %S A289563 1,3936,8895024,15094625920,21336320693400,26506772152211520, %T A289563 29887990556174431424,31237788209244729015552, %U A289563 30709242534935581933885740,28700724444538653431660487520,25706227251014342788669659769056,22202613798662970539127791744222592 %N A289563 Coefficients of 1/(q*(j(q)-1728))^4 where j(q) is the elliptic modular invariant. %H A289563 Seiichi Manyama, Table of n, a(n) for n = 0..361 %F A289563 G.f.: Product_{n>=1} (1-q^n)^(-4*A289061(n)). %F A289563 a(n) ~ c * exp(2*Pi*n) * n^7, where c = Gamma(3/4)^32 * exp(8*Pi) / (55540601303040 * Pi^8) = 0.0001042996202910562374208781457852661312263780276025385904... - _Vaclav Kotesovec_, Mar 07 2018 %t A289563 CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-4), {x, 0, 20}], x] (* _Vaclav Kotesovec_, Mar 07 2018 *) %Y A289563 (q*(j(q)-1728))^(k/24): this sequence (k=-96), A289562 (k=-72), A289561 (k=-48), A289417 (k=-24), A289416 (k=-1), A106203 (k=1), A289330 (k=2), A289331 (k=3), A289332 (k=4), A289333 (k=5), A289334 (k=6), A007242 (k=12), A289063 (k=24). %Y A289563 Cf. A289061. %K A289563 nonn %O A289563 0,2 %A A289563 _Seiichi Manyama_, Jul 08 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE