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Search: id:A006352
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| A006352 |
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Coefficients in expansion of Eisenstein series E_2 (also called E_1 or G_2).
(Formerly M5145)
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+0
20
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| 1, -24, -72, -96, -168, -144, -288, -192, -360, -312, -432, -288, -672, -336, -576, -576, -744, -432, -936, -480, -1008, -768, -864, -576, -1440, -744, -1008, -960, -1344, -720, -1728, -768, -1512, -1152, -1296, -1152, -2184, -912, -1440, -1344, -2160, -1008, -2304, -1056, -2016, -1872, -1728
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Expansion of Ramanujan's function P(q).
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
F. Beukers, Another congruence for the Apery numbers. J. Number Theory 25 (1987), no. 2, 201-210.
R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, NJ, 1962, p. 53.
N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 1984, see pp. 111 and 113.
M. Kaneko and D. Zagier, Supersingular j-invariants, hypergeometric series and Atkin's orthogonal polynomials, pp. 97-126 of D. A. Buell and J. T. Teitelbaum, eds., Computational Perspectives on Number Theory, Amer. Math. Soc., 1998.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..1000
H. Ochiai, Counting functions for branched covers of elliptic curves and quasi-modular forms
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Index entries for sequences related to Eisenstein series
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FORMULA
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n-th term is -24*sigma(n), for n>0.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)=u1^2+4*u2^2+9*u3^2+36*u6^2-8*u1*u2+6*u1*u3+24*u2*u6-72*u3*u6 . - Michael Somos May 29 2005
G.f.: 1-24(Sum_{k>0} kx^k/(1-x^k)).
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MAPLE
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E := proc(k) local n, t1; t1 := 1-(2*k/bernoulli(k))*add(sigma[k-1](n)*q^n, n=1..60); series(t1, q, 60); end; E(2);
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PROGRAM
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(PARI) a(n)=if(n<1, n==0, -24*sigma(n))
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CROSSREFS
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Cf. A006352 (E_2), A004009 (E_4), A013973 (E_6), A008410 (E_8), A013974 (E_10), A029828 (E_12), A058550 (E_14), A029829 (E_16), A029830 (E_20), A029831 (E_24).
Cf. A076835.
Sequence in context: A069174 A124717 A126378 this_sequence A143337 A090860 A064200
Adjacent sequences: A006349 A006350 A006351 this_sequence A006353 A006354 A006355
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KEYWORD
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sign,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
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