Search: id:A013974
Results 1-1 of 1 results found.

%I A013974
%S A013974 1,264,135432,5196576,69341448,515625264,2665843488,10653352512,
%T A013974 35502821640,102284205672,264515760432,622498190688,1364917062432,
%U A013974 2799587834736,5465169838656,10149567696576,18177444679944
%V A013974 1,-264,-135432,-5196576,-69341448,-515625264,-2665843488,-10653352512,
%W A013974 -35502821640,-102284205672,-264515760432,-622498190688,-1364917062432,
%X A013974 -2799587834736,-5465169838656,-10149567696576,-18177444679944
%N A013974 Eisenstein series E_10(q) (alternate convention E_5(q)).
%D A013974 R. C. Gunning, Lectures on Modular Forms. Princeton Univ. Press, Princeton, 
               NJ, 1962, p. 53.
%D A013974 N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer-Verlag, 
               1984, see p. 111.
%H A013974 T. D. Noe, <a href="b013974.txt">Table of n, a(n) for n=0..1000</a>
%H A013974 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 A013974 <a href="Sindx_Ed.html#Eisen">Index entries for sequences related to 
               Eisenstein series</a>
%F A013974 sum_{n=0...infinity} a(n)/exp(Pi)^(2n) = 0 or is very close to 0. - Gerald 
               McGarvey (Gerald.McGarvey(AT)comcast.net), Jan 25 2005
%F A013974 G.f. is a period 1 Fourier series which satisfies f(-1 / t) = - (t/i)^10 
               * f(t) where q = exp(2 pi i t). - Michael Somos Dec 30 2008
%e A013974 1 - 264*q - 135432*q^2 - 5196576*q^3 - 69341448*q^4 - 515625264*q^5 + 
               ...
%p A013974 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(10);
%o A013974 (PARI) a(n)=if(n<1,n==0,-264*sigma(n,9))
%Y A013974 Cf. A008410.
%Y A013974 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 A013974 Convolution of A004009 and A013973.
%Y A013974 Sequence in context: A022043 A035315 A107507 this_sequence A145639 A116501 
               A151602
%Y A013974 Adjacent sequences: A013971 A013972 A013973 this_sequence A013975 A013976 
               A013977
%K A013974 sign
%O A013974 0,2
%A A013974 N. J. A. Sloane (njas(AT)research.att.com).

Search completed in 0.001 seconds