%I A118271
%S A118271 1,1,3,5,3,6,15,8,3,23,18,12,15,14,24,30,3,18,69,20,18,40,36,24,15,31,
%T A118271 42,77,24,30,90,32,3,60,54,48,69,38,60,70,18,42,120,44,36,138,72,48,15,
%U A118271 57,93,90,42,54,231,72,24,100,90,60,90,62,96,184,3,84,180,68,54,120,144
%V A118271 1,1,-3,-5,-3,6,15,8,-3,-23,-18,12,15,14,-24,-30,-3,18,69,20,-18,-40,-36,
               24,15,31,-42,
%W A118271 -77,-24,30,90,32,-3,-60,-54,48,69,38,-60,-70,-18,42,120,44,-36,-138,-72,
               48,15,57,-93,
%X A118271 -90,-42,54,231,72,-24,-100,-90,60,90,62,-96,-184,-3,84,180,68,-54,-120,
               -144
%N A118271 Expansion of (9theta_4(q^3)^4-theta_4(q)^4)/8 in powers of q.
%F A118271 Expansion of eta(q^2)^5*et(q^3)^3/(eta(q)eta(q^6)^3) in powers of q.
%F A118271 Euler transform of period 6 sequence [ 1, -4, -2, -4, 1, -4, ...].
%F A118271 a(n) is multiplicative with a(2^e) = -3 if e>0, a(3^e) = 4-3^(e+1), a(p^e) 
               = (p^(e+1)-1)/(p-1) if p>3.
%o A118271 (PARI) {a(n)=if(n<0, 0, polcoeff( sum(k=1, sqrtint(n), 2*(-x)^k^2, 1+x*O(x^n))^4 
               -9*sum(k=1, sqrtint(n\3), 2*(-x^3)^k^2, 1+x*O(x^n))^4, n)/-8)}
%o A118271 (PARI) {a(n)= if(n<1, n==0, -(-1)^n*( sumdiv(n, d, d*(1-if(d%3==0,3)-if(d%4==0,
               1)+if(d%12==0,3)))))}
%o A118271 (PARI) {a(n)=local(A, p, e); if(n<1, n==0, A=factor(n); prod( k=1, matsize(A)[1], 
               if(p=A[k, 1], e=A[k, 2]; if(p==2, -3, if(p==3, 4-3^(e+1), (p^(e+1)-1)/
               (p-1))))))}
%o A118271 (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^5*eta(x^3+A)^3/ 
               eta(x+A)/ eta(x^6+A)^3, n))}
%Y A118271 A118272(n)=-a(3n+2)/3. A109506(3n)=a(3n). A109056(3n+1)=a(3n+1).
%Y A118271 Sequence in context: A134429 A100667 A096438 this_sequence A095366 A029604 
               A079602
%Y A118271 Adjacent sequences: A118268 A118269 A118270 this_sequence A118272 A118273 
               A118274
%K A118271 sign,mult
%O A118271 0,3
%A A118271 Michael Somos, Apr 21 2006