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A282048 Coefficients in q-expansion of E_4^5*E_6, where E_4 and E_6 are respectively the Eisenstein series A004009 and A013973. 5
1, 696, -34632, -167186976, -64422848328, -11387712944304, -1037073232984608, -48892286706157632, -1378097272692189000, -26188038166214133672, -364779879415169299632, -3952277018332870144608, -34798618196377082329632, -257403706082325167732976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

G. E. Andrews and B. C. Berndt, Ramanujan's lost notebook, Part III, Springer, New York, 2012, See p. 208.

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..1000

FORMULA

-24 * A281959(n) = 657931 * a(n) - 457920000 * A037947(n) for n > 0.

MATHEMATICA

terms = 14;

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}];

E4[x]^5*E6[x] + O[x]^terms // CoefficientList[#, x]& (* Jean-Fran├žois Alcover, Feb 27 2018 *)

CROSSREFS

Cf. A004009 (E_4), A013973 (E_6), A013974 (E_4*E_6 = E_10), A058550 (E_4^2*E_6 = E_14), A282000 (E_4^3*E_6), A282047 (E_4^4*E_6), this sequence (E_4^5*E_6).

Cf. A037947, A281959, A281979.

Sequence in context: A048426 A209731 A222782 * A163008 A282549 A069330

Adjacent sequences:  A282045 A282046 A282047 * A282049 A282050 A282051

KEYWORD

sign

AUTHOR

Seiichi Manyama, Feb 05 2017

STATUS

approved

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Last modified September 30 14:38 EDT 2022. Contains 357106 sequences. (Running on oeis4.)