Search: id:A006352
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%I A006352 M5145
%S A006352 1,24,72,96,168,144,288,192,360,312,432,288,672,336,576,576,744,432,
%T A006352 936,480,1008,768,864,576,1440,744,1008,960,1344,720,1728,768,1512,
%U A006352 1152,1296,1152,2184,912,1440,1344,2160,1008,2304,1056,2016,1872,1728
%V A006352 1,-24,-72,-96,-168,-144,-288,-192,-360,-312,-432,-288,-672,-336,-576,
               -576,-744,-432,
%W A006352 -936,-480,-1008,-768,-864,-576,-1440,-744,-1008,-960,-1344,-720,-1728,
               -768,-1512,
%X A006352 -1152,-1296,-1152,-2184,-912,-1440,-1344,-2160,-1008,-2304,-1056,-2016,
               -1872,-1728
%N A006352 Coefficients in expansion of Eisenstein series E_2 (also called E_1 or 
               G_2).
%C A006352 Expansion of Ramanujan's function P(q).
%D A006352 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006352 F. Beukers, Another congruence for the Apery numbers. J. Number Theory 
               25 (1987), no. 2, 201-210.
%D A006352 R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, 
               NJ, 1962, p. 53.
%D A006352 N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 
               1984, see pp. 111 and 113.
%D A006352 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.
%H A006352 T. D. Noe, <a href="b006352.txt">Table of n, a(n) for n=0..1000</a>
%H A006352 H. Ochiai, <a href="http://arXiv.org/abs/math-ph/9909023">Counting functions 
               for branched covers of elliptic curves and quasi-modular forms</a>
%H A006352 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               EisensteinSeries.html">Link to a section of The World of Mathematics.</
               a>
%H A006352 <a href="Sindx_Ed.html#Eisen">Index entries for sequences related to 
               Eisenstein series</a>
%F A006352 n-th term is -24*sigma(n), for n>0.
%F A006352 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
%F A006352 G.f.: 1-24(Sum_{k>0} kx^k/(1-x^k)).
%p A006352 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);
%o A006352 (PARI) a(n)=if(n<1,n==0,-24*sigma(n))
%Y A006352 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).
%Y A006352 Cf. A076835.
%Y A006352 Sequence in context: A069174 A124717 A126378 this_sequence A143337 A090860 
               A064200
%Y A006352 Adjacent sequences: A006349 A006350 A006351 this_sequence A006353 A006354 
               A006355
%K A006352 sign,easy,nice
%O A006352 0,2
%A A006352 N. J. A. Sloane (njas(AT)research.att.com).
%E A006352 More terms from Erich Friedman (erich.friedman(AT)stetson.edu).

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