cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-6 of 6 results.

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

Views

Author

Michael Somos, Apr 25 2005

Keywords

Links

Crossrefs

(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).
Cf. A000521, A289061.

Programs

  • Mathematica
    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 *)
  • PARI
    {a(n)=if(n<0,0, polcoeff( ((ellj(x+x^2*O(x^n))-1728)*x)^(1/24),n))}

Formula

G.f.: Product_{k>=1} (1-q^k)^(A289061(k)/24). - Seiichi Manyama, Jul 02 2017
a(n) ~ c * exp(2*Pi*n) / n^(13/12), where c = -2^(1/12) * Pi^(25/12) * exp(-Pi/12) / (3^(13/12) * Gamma(2/3)^2 * Gamma(3/4)^(7/3) * Gamma(1/12)) = -0.0794786705643291777786030631826408355507134016936764993676699378963... - Vaclav Kotesovec, Mar 07 2018

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

Views

Author

Seiichi Manyama, Jul 06 2017

Keywords

Links

Crossrefs

(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).
Cf. A289061, A289209.

Programs

  • Mathematica
    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 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(-A289061(n)).
a(n) ~ c * exp(2*Pi*n) * n, where c = Gamma(3/4)^8 * exp(2*Pi) / (324 * Pi^2) = 0.851487576721136974981670736748581778120097667011853803210435262759745... - 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

Views

Author

Seiichi Manyama, Jul 08 2017

Keywords

Links

Crossrefs

(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).
Cf. A289061.

Programs

  • Mathematica
    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 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(-2*A289061(n)).
a(n) ~ c * exp(2*Pi*n) * n^3, where c = Gamma(3/4)^16 * exp(4*Pi) / (629856 * Pi^4) = 0.120838515551739021017044909469013807578104459775498957232984908667972... - Vaclav Kotesovec, Mar 07 2018

A289562 Coefficients of 1/(q*(j(q)-1728))^3 where j(q) is the elliptic modular invariant.

Original entry on oeis.org

1, 2952, 5218884, 7138351488, 8319960432666, 8678332561127616, 8338315178481134040, 7518590274496806176256, 6444205834302869333758299, 5298802621872639665867604832, 4208666443076672300677008045636, 3246069554930472099322915758511872
Offset: 0

Views

Author

Seiichi Manyama, Jul 08 2017

Keywords

Links

Crossrefs

(q*(j(q)-1728))^(k/24): A289563 (k=-96), this sequence (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).
Cf. A289061.

Programs

  • Mathematica
    CoefficientList[Series[((256/QPochhammer[-1, x]^8 + x*QPochhammer[-1, x]^16/256)^3 - 1728*x)^(-3), {x, 0, 20}], x] (* Vaclav Kotesovec, Mar 07 2018 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(-3*A289061(n)).
a(n) ~ c * exp(2*Pi*n) * n^5, where c = Gamma(3/4)^24 * exp(6*Pi) / (4081466880 * Pi^6) = 0.0051446247390864841578336638645072392120317488530740050289688... - 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

Views

Author

Seiichi Manyama, Jul 08 2017

Keywords

Links

Crossrefs

(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).
Cf. A289061.

Programs

  • Mathematica
    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 *)

Formula

G.f.: Product_{n>=1} (1-q^n)^(-4*A289061(n)).
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

A305696 Coefficients of (q*(j(q)-744))^(-1/4) where j(q) is the elliptic modular invariant.

Original entry on oeis.org

1, 0, -49221, -5373440, 5840692110, 1317368987136, -769081921703395, -285861152927176704, 99587019847435059600, 58472021328782000084480, -11456674101843809483255526, -11455351916487867258761894400, 892125673948866841204086469705
Offset: 0

Views

Author

Seiichi Manyama, Jun 08 2018

Keywords

Links

Crossrefs

(q*(j(q)-744))^(k/4): A305699 (k=-4), A305698 (k=-2), this sequence (k=-1), A304020 (k=1), A305697 (k=2).
Cf. A000521 (j), A014708 (j-744), A289397, A289416, A302407.

Programs

  • Mathematica
    CoefficientList[Series[((2^16 + x*QPochhammer[-1, x]^24)^3/(2*QPochhammer[-1, x])^24 - 744*x)^(-1/4), {x, 0, 15}], x] (* Vaclav Kotesovec, Jun 09 2018 *)

Formula

G.f.: Product_{k>0} (1 - x^k)^(A302407(k)/4).
Showing 1-6 of 6 results.

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