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 1-7 of 7 results.

A029831 Eisenstein series E_24(q) (alternate convention E_12(q)), multiplied by 236364091.

Original entry on oeis.org

236364091, 131040, 1099243323360, 12336522153621120, 9221121336284413920, 1562118530273437631040, 103486260766565509822080, 3586400651444203277717760, 77352372210526124884754400, 1161399411211600265764157280
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), A279892 (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), this sequence (236364091*E_24).
Cf. A282330 (E_4^6), A282332 (E_4^3*E_6^2), A282331 (E_6^4).

Programs

  • Mathematica
    terms = 10;
E24[x_] = 236364091 + 131040*Sum[k^23*x^k/(1 - x^k), {k, 1, terms}];
E24[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
  • PARI
    a(n)=if(n<1,236364091*(n==0),131040*sigma(n,23))

Formula

a(n) = 49679091*A282330(n) + 176400000*A282332(n) + 10285000*A282331(n). - Seiichi Manyama, Feb 12 2017

A029830 Eisenstein series E_20(q) (alternate convention E_10(q)), multiplied by 174611.

Original entry on oeis.org

174611, 13200, 6920614800, 15341851377600, 3628395292275600, 251770019531263200, 8043563916910526400, 150465416446925500800, 1902324110996589786000, 17831242688625346952400, 132000251770026451864800, 807299993919072011054400, 4217144038884527916580800, 19297347832955888660949600
Offset: 0

Views

Author

N. J. A. Sloane

Keywords

References

  • J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), A279892 (43867*E_18), this sequence (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24).
Cf. A282015 (E_4^5), A282292 (E_4^2*E_6^2 = E_10^2).

Programs

  • Mathematica
    terms = 14;
E20[x_] = 174611 + 13200*Sum[k^19*x^k/(1 - x^k), {k, 1, terms}];
E20[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 27 2018 *)
  • PARI
    a(n)=if(n<1,174611*(n==0),13200*sigma(n,19))

Formula

a(n) = 53361*A282015(n) + 121250*A282292(n). - Seiichi Manyama, Feb 11 2017

A279892 Eisenstein series E_18(q) (alternate convention E_9(q)), multiplied by 43867.

Original entry on oeis.org

43867, -28728, -3765465144, -3709938631392, -493547047383096, -21917724609403728, -486272786232443616, -6683009405824511424, -64690198594597187640, -479102079577959825624, -2872821917728374840144, -14520482234727711482016, -63736746640768788267744
Offset: 0

Views

Author

Seiichi Manyama, Dec 22 2016

Keywords

References

  • J.-P. Serre, Course in Arithmetic, Chap. VII, Section 4.

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), this sequence (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24).
Cf. A282000 (E_4^3*E_6), A282253 (E_6^3).

Programs

  • Mathematica
    terms = 13;
E18[x_] = 43867 - 28728*Sum[k^17*x^k/(1 - x^k), {k, 1, terms}];
E18[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

G.f.: 43867 - 28728 * Sum_{i>=1} sigma_17(i)q^i where sigma_17(n) is A013965.
a(n) = 38367*A282000(n) + 5500*A282253(n). - Seiichi Manyama, Feb 11 2017

A282356 Eisenstein series E_26(q) (alternate convention E_13(q)), multiplied by 657931.

Original entry on oeis.org

657931, -24, -805306392, -20334926626656, -27021598569529368, -7152557373046875024, -682326933054044766048, -32185646871935157619392, -906694391732570450559000, -17229551704624797057112632, -240000007152557373852181392
Offset: 0

Views

Author

Seiichi Manyama, Feb 13 2017

Keywords

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), A279892 (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24), this sequence (657931*E_26).
Cf. A282048 (E_4^5*E_6), A282357 (E_4^2*E_6^3).

Programs

  • Mathematica
    terms = 11;
E26[x_] = 657931 - 24*Sum[k^25*x^k/(1 - x^k), {k, 1, terms}];
E26[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

a(n) = 392931*A282048(n) + 265000*A282357(n).

A282401 Eisenstein series E_28(q) (alternate convention E_14(q)), multiplied by 3392780147.

Original entry on oeis.org

3392780147, 6960, 934155393840, 53074158495516480, 125380214560150002480, 51856040954589843756960, 7123493021854278627673920, 457358042050198589771226240, 16828247534415852672059972400, 404722169541211889603611092720
Offset: 0

Views

Author

Seiichi Manyama, Feb 14 2017

Keywords

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), A279892 (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24), A282356 (657931*E_26), this sequence (3392780147*E_28).
Cf. A282402 (E_4^7), A282403 (E_4^4*E_6^2), A282404 (E_4*E_6^4).

Programs

  • Mathematica
    terms = 10;
E28[x_] = 3392780147 + 6960*Sum[k^27*x^k/(1 - x^k), {k, 1, terms}];
E28[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

a(n) = 489693897*A282402(n) + 2507636250*A282403(n) + 395450000*A282404(n).

A282182 Eisenstein series E_30(q) (alternate convention E_15(q)), multiplied by 1723168255201.

Original entry on oeis.org

1723168255201, -171864, -92268782591832, -11795091175438423776, -49536425459206569762648, -32012164592742919922046864, -6332441368275869747902027488, -553385882817076320573218661312, -26594665913504249904864455466840
Offset: 0

Views

Author

Seiichi Manyama, Feb 16 2017

Keywords

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), A279892 (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24), A282356 (657931*E_26), A282401 (3392780147*E_28), this sequence (1723168255201*E_30).
Cf. A282382 (E_4^6*E_6), A282461 (E_4^3*E_6^3), A282433 (E_6^5).

Programs

  • Mathematica
    terms = 9;
E30[x_] = 1723168255201 - 171864*Sum[k^29*x^k/(1 - x^k), {k, 1, terms}];
E30[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

a(n) = 815806500201*A282382(n) + 881340705000*A282461(n) + 26021050000*A282433(n).

A282540 Eisenstein series E_32(q) (alternate convention E_16(q)), multiplied by 7709321041217.

Original entry on oeis.org

7709321041217, 32640, 70093866303360, 20160859654708062720, 150525431711563807489920, 151991844177246093750032640, 43295116458269350559666465280, 5149788469617367127914995164160, 323250903208723929093223124860800
Offset: 0

Views

Author

Seiichi Manyama, Feb 17 2017

Keywords

Links

Crossrefs

Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (691*E_12), A058550 (E_14), A029829 (3617*E_16), A279892 (43867*E_18), A029830 (174611*E_20), A279893 (77683*E_22), A029831 (236364091*E_24), A282356 (657931*E_26), A282401 (3392780147*E_28), A282182 (1723168255201*E_30), this sequence (7709321041217*E_32).
Cf. A282474 (E_4^8), A282541 (E_4^5*E_6^2), A282543 (E_4^2*E_6^4).

Programs

  • Mathematica
    terms = 9;
E32[x_] = 7709321041217 + 32640*Sum[k^31*x^k/(1 - x^k), {k, 1, terms}];
E32[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-François Alcover, Feb 26 2018 *)

Formula

a(n) = 764412173217*A282474(n) + 5323905468000 * A282541(n) + 1621003400000 * A282543(n).
Showing 1-7 of 7 results.

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

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