1,2

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 102.

Index entries for reversions of series

R. S. Maier, On Rationally Parametrized Modular Equations see page 4 equation (4)

REVERT(A005149).

Euler transform of period 2 sequence [24, 0, 24, 0, ...]. - Michael Somos Mar 19 2004

Expansion of (lambda/16)^2/(1-lambda) in powers of q^2. - Michael Somos Nov 19 2005

Expansion of q/chi(-q)^24 in powers of q where chi() is a Ramanujan theta function.

G.f.: x*Product_{k>0} (1+x^k)^24.

G.f.: (theta_2(q)*theta_3(q)/(2*theta_4(q)^2))^4.

G.f.: (theta_2(q^(1/2))^2/(4*theta_4(q^(1/2))theta_3(q^(1/2))))^4.

G.f. A(x) satisfies 0 = f(A(x), A(x^2)) where f(u, v) = u^2 - v - 48*u*v - 4096*u*v^2. - Michael Somos Mar 19 2004

G.f. is a Fourier series which satisfies f(-1/(2 t)) = (1/4096) / f(t) where q = exp(2 pi i t). - Michael Somos Aug 19 2007

j(q) = (f(q) + 16)^3 / f(q), j(q^2) = (f(q) + 256)^3 / f(q)^2 where j(q) is g.f. for A000521 and f(q) is 4096 times g.f. a(n). - Michael Somos Oct 01 2007

q + 24*q^2 + 300*q^3 + 2624*q^4 + 18126*q^5 + 105504*q^6 + 538296*q^7 + ...

q*mul((1+q^m)^24, m=1..30);

(PARI) a(n)=polcoeff(x*prod(k=1, n, 1+x^k, 1+x*O(x^n))^24, n)

(PARI) a(n)=local(A, A2, m); if(n<0, 0, A=x+O(x^2); m=1; while(m<=n, m*=2; A=subst(A, x, x^2); A2=A*(1+16*A); A=8*A2+(1+32*A)*sqrt(A2)); polcoeff(A+16*A^2, n))

(PARI) a(n)=local(A); if(n<1, 0, n--; A=x*O(x^n); polcoeff((eta(x^2+A)/eta(x+A))^24, n))

Adjacent sequences: A014100 A014101 A014102 this_sequence A014104 A014105 A014106

Sequence in context: A056285 A010976 A100130 this_sequence A000552 A125436 A096821

nonn

njas

More terms from Michael Somos, Nov 24, 2001