%I A034320
%S A034320 1,1,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64,76,89,104,122,141,
%T A034320 164,191,220,254,293,336,385,442,504,575,656,745,846,960,1086,1228,1388,
%U A034320 1564,1762,1984,2228,2501,2806,3142,3516,3932,4390,4898,5462,6082
%N A034320 Expansion of Hauptmodul for Gamma_0(50)+50.
%C A034320 Expansion of (eta(q^2)eta(q^25))/(eta(q)eta(q^50)) in powers of q. - 
               Michael Somos, Sep 20 2004
%C A034320 Euler transform of period 50 sequence [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
               0,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,
               1,0,...]. - Michael Somos, Sep 20 2004
%C A034320 Essentially McKay-Thompson series of class 50a for Monster.
%D A034320 F. Calegari, Review of "A first Course in modular forms" by F. Diamond 
               and J. Shurman, Bull. Amer. Math. Soc., 43 (No. 3, 2006), 415-421. 
               See p. 418
%H A034320 <a href="Sindx_Mat.html#McKay_Thompson">Index entries for McKay-Thompson 
               series for Monster simple group</a>
%H A034320 I. Chen and N. Yui, <a href="http://www.math.sfu.ca/~ichen/pub.html">
               Singular values of Thompson series</a>. In Groups, difference sets 
               and the Monster (Columbus, OH, 1993), pp. 255-326, Ohio State University 
               Mathematics Research Institute Publications, 4, de Gruyter, Berlin, 
               1996.
%F A034320 G.f.: 1/x(Product_{k>0} (1+x^k)/(1+x^(25k))).
%F A034320 Expansion of (q^-1) *chi(-q^25)/ chi(-q) in powers of q where chi() is 
               a Ramanujan theta function. - Michael Somos Jun 09 2007
%F A034320 G.f. is Fourier series of a weight 0 level 50 modular form. f(-1/ (50 
               t)) = f(t) where q = exp(2 pi i t). - Michael Somos Jun 09 2007
%F A034320 G.f. A(x) satisfies 0= f(A(x), A(x^2), A(x^4)) where f(u, v, w)= u^2*v 
               +2*u*w +2*u*v^2*w +v*w^2 -v^2 -u^2*w^2. - Michael Somos Jun 09 2007
%e A034320 q^-1 + 1 + q + 2*q^2 + 2*q^3 + 3*q^4 + 4*q^5 + 5*q^6 + 6*q^7 + 8*q^8 
               + ...
%o A034320 (PARI) a(n)=local(A); if(n<-1,0, n++; A=1+x*O(x^n); polcoeff( prod(k=1,
               n,1+x^k,A)/prod(k=1,n\25,1+x^(25*k),A),n)) /* Michael Somos, Sep 
               20 2004 */
%o A034320 (PARI) a(n)=local(A); if(n<-1,0, n++; A=x*O(x^n); polcoeff( eta(x^2+A)*eta(x^25+A)/
               (eta(x+A)*eta(x^50+A)),n)) /* Michael Somos, Sep 20 2004 */
%Y A034320 Cf. A034321.
%Y A034320 A058703(n)=a(n) if n nonzero.
%Y A034320 Sequence in context: A034150 A034321 A058703 this_sequence A000009 A081360 
               A117409
%Y A034320 Adjacent sequences: A034317 A034318 A034319 this_sequence A034321 A034322 
               A034323
%K A034320 nonn
%O A034320 -1,4
%A A034320 N. J. A. Sloane (njas(AT)research.att.com).