A289368
Coefficients in expansion of (E_6^2/E_4^3)^(1/24).
Original entry on oeis.org
1, -72, -6048, -4217184, -1264437504, -606533479920, -251777443450752, -117085712395216320, -53634689421870422016, -25408429618361083967592, -12110787335129301116994240, -5854620911089647830793873696
Offset: 0
(E_6^2/E_4^3)^(k/288):
A289366 (k=1),
A296609 (k=2),
A296614 (k=3),
A296652 (k=4),
A297021 (k=6),
A299422 (k=8),
A299862 (k=9), this sequence (k=12),
A299856 (k=16),
A299857 (k=18),
A299858 (k=24),
A299863 (k=32),
A299859 (k=36),
A299860 (k=48),
A299861 (k=72),
A299414 (k=96),
A299413 (k=144),
A289210 (k=288).
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nmax = 20; CoefficientList[Series[((1 - 504*Sum[DivisorSigma[5,k]*x^k, {k, 1, nmax}])^2 / (1 + 240*Sum[DivisorSigma[3,k]*x^k, {k, 1, nmax}])^3)^(1/24), {x, 0, nmax}], x] (* Vaclav Kotesovec, Jul 08 2017 *)
A294974
Coefficients in expansion of (E_2^4/E_4)^(1/8).
Original entry on oeis.org
1, -42, 4032, -659904, 118064226, -22406634432, 4407587356032, -888750999070464, 182478248639753472, -37986867560948245674, 7994272624037726124672, -1697243410477799687716416, 362963150140702802158191360, -78095916585903527021840348352
Offset: 0
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terms = 14;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
(E2[x]^4/E4[x])^(1/8) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
Original entry on oeis.org
30, 11775, 4261790, 1712983575, 733856931102, 327479190724415, 150310619778297630, 70428822637214055855, 33523597190372498303390, 16156445902947621421555071, 7865129058155113639991368350, 3860735065245244345161225213335
Offset: 1
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terms = 12;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
E8[x_] = 1 + 480*Sum[k^7*x^k/(1 - x^k), {k, 1, terms}];
a[n_] := (1/(24 n))*Sum[MoebiusMu[n/d]*SeriesCoefficient[E8[x]/E6[x] - E4[x]/E2[x], {x, 0, d}], {d, Divisors[n]}];
Array[a, terms] (* Jean-François Alcover, Feb 26 2018 *)
A295788
Coefficients in expansion of (E_10/E_2^10)^(1/4).
Original entry on oeis.org
1, -6, -41652, -11504904, -4378103178, -1652544433080, -700184843900712, -302796005909941632, -136251754253507319300, -62421509259448987324542, -29147951871527035454309160, -13787807362002100397282325912
Offset: 0
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terms = 12;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E10[x_] = 1 - 264*Sum[k^9*x^k/(1 - x^k), {k, 1, terms}];
(E10[x]/E2[x]^10)^(1/4) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A299712
Coefficients in expansion of (E_14/E_2^14)^(1/4).
Original entry on oeis.org
1, 78, -44928, -14386944, -5323508814, -1996794824544, -833028042023424, -358702721913389568, -160514702770156497360, -73334654476723097306706, -34151846554093744054455552, -16125009656471947012310740224
Offset: 0
-
terms = 12;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E4[x_] = 1 + 240*Sum[k^3*x^k/(1 - x^k), {k, 1, terms}];
E10[x_] = 1 - 264*Sum[k^9*x^k/(1 - x^k), {k, 1, terms}];
E14[x_] = E4[x]*E10[x];
(E14[x]/E2[x]^14)^(1/4) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
A294979
Coefficients in expansion of (E_2^6/E_6)^(1/12).
Original entry on oeis.org
1, 30, 12240, 4620000, 1915684770, 839549366208, 381374756189280, 177631327935911040, 84272487587664762240, 40549569894460426101150, 19730577674798681251391712, 9687875889040210133058857760, 4792614349874614536514510456320
Offset: 0
-
terms = 13;
E2[x_] = 1 - 24*Sum[k*x^k/(1 - x^k), {k, 1, terms}];
E6[x_] = 1 - 504*Sum[k^5*x^k/(1 - x^k), {k, 1, terms}];
(E2[x]^6/E6[x])^(1/12) + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)
Showing 1-6 of 6 results.
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