A106203
Coefficients of ((j(q)-1728)q)^(1/24) where j(q) is the elliptic modular invariant.
Original entry on oeis.org
1, -41, -11128, -3785793, -1476507895, -618962022329, -271503819749095, -122857395553223337, -56870247894888518054, -26784343611333662213130, -12787694574831980406719382, -6172809198874485994313412898
Offset: 0
(q*(j(q)-1728))^(k/24):
A289563 (k=-96),
A289562 (k=-72),
A289561 (k=-48),
A289417 (k=-24),
A289416 (k=-1), this sequence (k=1),
A289330 (k=2),
A289331 (k=3),
A289332 (k=4),
A289333 (k=5),
A289334 (k=6),
A007242 (k=12),
A289063 (k=24).
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CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(1/24), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)
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{a(n)=if(n<0,0, polcoeff( ((ellj(x+x^2*O(x^n))-1728)*x)^(1/24),n))}
A289417
Coefficients of 1/(q*(j(q)-1728)) where j(q) is the elliptic modular invariant.
Original entry on oeis.org
1, 984, 771372, 543802432, 361216628430, 230920762687776, 143732944930479800, 87718753215371355648, 52729710063184125105381, 31319171802847165756090320, 18421996714811488321383528228, 10748837396953435386200311855872
Offset: 0
(q*(j(q)-1728))^(k/24):
A289563 (k=-96),
A289562 (k=-72),
A289561 (k=-48), this sequence (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).
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CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-1), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)
A289416
Coefficients of (q*(j(q)-1728))^(-1/24) where j(q) is the elliptic modular invariant.
Original entry on oeis.org
1, 41, 12809, 4767210, 1969719570, 861799083811, 391094324350380, 182038077972154741, 86322373755372340110, 41521193849940130872000, 20197774625594843441436930, 9915082544034345319047507780
Offset: 0
(q*(j(q)-1728))^(k/24):
A289563 (k=-96),
A289562 (k=-72),
A289561 (k=-48),
A289417 (k=-24), this sequence (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).
-
CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-1/24), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)
A289561
Coefficients of 1/(q*(j(q)-1728))^2 where j(q) is the elliptic modular invariant.
Original entry on oeis.org
1, 1968, 2511000, 2605664960, 2387651205420, 2011663789279200, 1594903822090229312, 1207416525204065938560, 881461062200198781904590, 624887481909094711741279120, 432393768184906363401468637728, 293171504960988659691658645670592
Offset: 0
(q*(j(q)-1728))^(k/24):
A289563 (k=-96),
A289562 (k=-72), this sequence (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).
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CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-2), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)
A289563
Coefficients of 1/(q*(j(q)-1728))^4 where j(q) is the elliptic modular invariant.
Original entry on oeis.org
1, 3936, 8895024, 15094625920, 21336320693400, 26506772152211520, 29887990556174431424, 31237788209244729015552, 30709242534935581933885740, 28700724444538653431660487520, 25706227251014342788669659769056, 22202613798662970539127791744222592
Offset: 0
(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).
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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 *)
Showing 1-5 of 5 results.