-1,4

Expansion of (eta(q^2)eta(q^25))/(eta(q)eta(q^50)) in powers of q. - Michael Somos, Sep 20 2004

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

Essentially McKay-Thompson series of class 50a for Monster.

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

Index entries for McKay-Thompson series for Monster simple group

I. Chen and N. Yui, Singular values of Thompson series. 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.

G.f.: 1/x(Product_{k>0} (1+x^k)/(1+x^(25k))).

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

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

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

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 + ...

(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 */

(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 */

Cf. A034321.

A058703(n)=a(n) if n nonzero.

Sequence in context: A034150 A034321 A058703 this_sequence A000009 A081360 A117409

Adjacent sequences: A034317 A034318 A034319 this_sequence A034321 A034322 A034323

nonn

N. J. A. Sloane (njas(AT)research.att.com).