%I A022569
%S A022569 1,4,10,24,51,100,190,344,601,1024,1702,2768,4422,6948,10752,16424,
%T A022569 24782,36972,54602,79872,115805,166540,237664,336720,473856,662596,
%U A022569 920934,1272728,1749407,2392268,3255410,4409344,5945730,7983388
%N A022569 Expansion of Product (1+q^m)^4; m=1..inf.
%C A022569 Expansion of chi(-q)^(-4) in powers of q where chi() is a Ramanujan theta 
               function.
%F A022569 Expansion of q^(-1/6) * (eta(q^2) / eta(q))^4 in powers of q.
%F A022569 Euler transform of period 2 sequence [ 4, 0, ...]. - Michael Somos Apr 
               26 2008
%F A022569 Given G.f. A(x) then B(x) = (A(x^6) * x)^2 satisfies 0 = f(B(x), B(x^2)) 
               where f(u, v) = v * (1 + 16 * u * v) - u^2. - Michael Somos Apr 26 
               2008
%F A022569 Given G.f. A(x) then B(x) = A(x^6) * x satisfies 0 = f(B(x), B(x^2), 
               B(x^4)) where f(u, v, w) = v * (u^2 - v) - 4 * w^2 * (u^2 + v). - 
               Michael Somos Apr 26 2008
%F A022569 G.f. is a period 1 Fourier series which satisfies f(-1/(72 t)) = (1/4) 
               / f(t) where q = exp(2 pi i t).
%e A022569 q + 4*q^7 + 10*q^13 + 24*q^19 + 51*q^25 + 100*q^31 + 190*q^37 + 344*q^43 
               + ...
%o A022569 (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 
               + A) / eta(x + A))^4, n))} /* Michael Somos Apr 26 2008 */
%Y A022569 Convolution inverse of A022599.
%Y A022569 Sequence in context: A058514 A001979 A128516 this_sequence A093831 A052365 
               A107659
%Y A022569 Adjacent sequences: A022566 A022567 A022568 this_sequence A022570 A022571 
               A022572
%K A022569 nonn
%O A022569 0,2
%A A022569 N. J. A. Sloane (njas(AT)research.att.com).