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 1-5 of 5 results.

A304020 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, -3417985269, -788396806656, 342234419865236, 132462307415526912, -36238724753334630039, -22802599804762047656960, 3430044089325166785294348, 3917150794938668128412249088, -180732068045239143713224620097
Offset: 0

Views

Author

Seiichi Manyama, Jun 08 2018

Keywords

Crossrefs

(q*(j(q)-744))^(k/4): A305699 (k=-4), A305698 (k=-2), A305696 (k=-1), this sequence (k=1), A305697 (k=2).
Cf. A000521 (j), A014708 (j-744), A106203, A106205, 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).

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

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).

A305697 Coefficients of (q*(j(q)-744))^(1/2) where j(q) is the elliptic modular invariant.

Original entry on oeis.org

1, 0, 98442, 10746880, -4413263697, -1047821432832, 376869391313174, 150580578862513152, -35577391320709928685, -23497935558209789278208, 2998297272257446799809386, 3754973355232751413790773248, -112875007087323495790855645044
Offset: 0

Views

Author

Seiichi Manyama, Jun 08 2018

Keywords

Crossrefs

(q*(j(q)-744))^(k/4): A305699 (k=-4), A305698 (k=-2), A305696 (k=-1), A304020 (k=1), this sequence (k=2).
Cf. A000521 (j), A014708 (j-744).

Programs

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

A305698 Coefficients of (q*(j(q)-744))^(-1/2) where j(q) is the elliptic modular invariant.

Original entry on oeis.org

1, 0, -98442, -10746880, 14104091061, 3163710154752, -2084259398665810, -764175960909112320, 294840080134539846210, 168738710694984764315648, -36893258480144387666915136, -35102639613834243676336481280
Offset: 0

Views

Author

Seiichi Manyama, Jun 08 2018

Keywords

Crossrefs

(q*(j(q)-744))^(k/4): A305699 (k=-4), this sequence (k=-2), A305696 (k=-1), A304020 (k=1), A305697 (k=2).
Cf. A000521 (j), A014708 (j-744).

Programs

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

A305760 Coefficients of 1/(q*(j(q)-720)) where j(q) is the elliptic modular invariant.

Original entry on oeis.org

1, -24, -196308, -12057152, 38590826190, 5667574866912, -7304962792606024, -1755598494902269440, 1325502689549152990437, 465173370338426065214640, -228213884020015849568089308, -112934890287321570650976240384
Offset: 0

Views

Author

Seiichi Manyama, Jun 10 2018

Keywords

Crossrefs

(q*(j(q)-720))^(m/24): this sequence (m=-24), A305758 (m=-1), A305756 (m=1).
Cf. A000521, A007240 (j(q)-720), A305699, A305757.

Formula

G.f.: Product_{k>0} (1 - x^k)^A305757(k).
Showing 1-5 of 5 results.