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.

Previous Showing 11-15 of 15 results.

A008699 Theta series of Niemeier lattice of type A_6^4.

Original entry on oeis.org

1, 168, 192528, 16815456, 397786704, 4630192560, 34416639936, 187487122368, 814893967440, 2975532395976, 9486531825120, 27053035734816, 70486174680768, 169930998266736, 384163653863808
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

Links

Crossrefs

Cf. A004009, A013973.
Cf. A008688 - A008698, A008700 - A008704.

Programs

  • Mathematica
    terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 49/72 E4[q]^3 + 23/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Formula

This series is the q-expansion of (49*E_4(z)^3 + 23*E_6(z)^2)/72. - Daniel D. Briggs, Nov 25 2011

A008701 Theta series of Niemeier lattice of type A_4^6.

Original entry on oeis.org

1, 120, 193680, 16803360, 397857360, 4629960720, 34416930240, 187487926080, 814889912400, 2975537850840, 9486537389280, 27053010073440, 70486192486080, 169931025998160, 384163634574720
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

Links

Crossrefs

Cf. A004009, A013973.
Cf. A008688 - A008700, A008702, A008703, A008704.

Programs

  • Mathematica
    terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 47/72 E4[q]^3 + 25/72 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Formula

This series is the q-expansion of (47*E_4(z)^3 + 25*E_6(z)^2)/72. - Daniel D. Briggs, Nov 25 2011

A008690 Theta series of Niemeier lattice of type D_12^2.

Original entry on oeis.org

1, 528, 183888, 16906176, 397256784, 4631931360, 34414462656, 187481094528, 814924380240, 2975491484496, 9486490093920, 27053228195136, 70486041140928, 169930790281056, 384163798531968
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

Links

Crossrefs

Cf. A008688, A008689, A008691 - A008704.

Programs

  • Mathematica
    terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 8/9 E4[q]^3 + 1/9 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Formula

This series is the q-expansion of 8/9 E_4(z)^3 + 1/9 E_6(z)^2. See A004009 and A013973. - Daniel D. Briggs, Nov 25 2011

A008692 Theta series of Niemeier lattice of type A_15 D_9.

Original entry on oeis.org

1, 384, 187344, 16869888, 397468752, 4631235840, 34415333568, 187483505664, 814912215120, 2975507849088, 9486506786400, 27053151211008, 70486094556864, 169930873475328, 384163740664704
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 407.

Links

Crossrefs

Cf. A008688, A008689, A008690, A008691, A008693 - A008704.

Programs

  • Mathematica
    terms = 15; E4[q_] := 1 + 240 Sum[DivisorSigma[3, n]*q^(2 n), {n, 1, terms}]; E6[q_] := 1 - 504 Sum[DivisorSigma[5, n]*q^(2 n), {n, 1, terms}]; s = 29/36 E4[q]^3 + 7/36 E6[q]^2 + O[q]^(3 terms); Partition[ CoefficientList[s, q], 2][[All, 1]][[1 ;; terms]] (* Jean-François Alcover, Jul 06 2017 *)

Formula

This series is the q-expansion of (29*E_4(z)^3 + 7*E_6(z)^2)/36. See A004009 and A013973. - Daniel D. Briggs, Nov 25 2011

A055766 Jacobi form of weight 12 and index 1 for Niemeier lattice of type A_1^24.

Original entry on oeis.org

1, 0, 0, 0, 46, 0, 0, 32384, 130548, 0, 0, 3674112, 9175896, 0, 0, 95659392, 188227998, 0, 0, 1143025664, 1959757320, 0, 0, 8506630272, 13293010632, 0, 0, 45762572288, 67073562688, 0, 0, 195389505792, 272567911572, 0, 0
Offset: 0

Views

Author

Kok Seng Chua (chuaks(AT)ihpc.nus.edu.sg), Jul 12 2000

Keywords

References

  • Eichler and Zagier, The Theory of Jacobi Forms, Birkhauser,1985.

Crossrefs

Cf. A008704, A055747, A003785.

Formula

E_8*E_{4, 1}-56*phi_12.
G.f.: b(z) - 56*c(z) where b(z) is the g.f. for A055747 and c(z) is the g.f. for A003785. - Sean A. Irvine, Apr 05 2022
Previous Showing 11-15 of 15 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.