Search: id:A131944
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%I A131944
%S A131944 1,1,5,1,6,5,8,1,23,6,12,5,14,8,30,1,18,23,20,6,40,12,24,5,31,14,77,8,
%T A131944 30,30,32,1,60,18,48,23,38,20,70,6,42,40,44,12,138,24,48,5,57,31,90,14,
%U A131944 54,77,72,8,100,30,60,30,62,32,184,1,84,60,68,18,120,48,72,23,74,38,155
%V A131944 1,1,-5,1,6,-5,8,1,-23,6,12,-5,14,8,-30,1,18,-23,20,6,-40,12,24,-5,31,
               14,-77,8,30,-30,
%W A131944 32,1,-60,18,48,-23,38,20,-70,6,42,-40,44,12,-138,24,48,-5,57,31,-90,14,
               54,-77,72,8,
%X A131944 -100,30,60,-30,62,32,-184,1,84,-60,68,18,-120,48,72,-23,74,38,-155
%N A131944 Expansion of (1-eta(q)^3 * eta(q^2)^3/( eta(q^3) * eta(q^6)))/3 in powers 
               of q.
%D A131944 N. J. Fine, Basic Hypergeometric Series and Applications, Amer. Math. 
               Soc., 1988; p. 84, Eq. (32.65).
%F A131944 Expansion of (1-b(q)*b(q^2))/3 where b() is a cubic AGM function.
%F A131944 a(n) is multiplicative with a(2^e) = 1, a(3^e) = 4- 3^(e+1), a(p^e) = 
               (p^(e+1)-1)/(p-1) if p>3.
%F A131944 G.f.: (1- Product_{k>0} ((1-x^k)* (1-x^(2k)))^3/( (1-x^(3k))* (1-x^(6k))))/
               3.
%F A131944 G.f.: Sum_{k>0} (6k-1)* x^(6k-1)/( 1-x^(6k-1)) -2*(6k-5)* x^(6k-3)/( 
               1-x^(6k-3)) +(6k-5)* x^(6k-5)/( 1-x^(6k-5)).
%e A131944 q + q^2 - 5*q^3 + q^4 + 6*q^5 - 5*q^6 + 8*q^7 + q^8 - 23*q^9 + 6*q^10 
               +...
%o A131944 (PARI) {a(n)= if(n<1, 0, sumdiv(n, d, d*((d%6==1)+ (d%6==5)- 2*(d%6==3))))}
%o A131944 (PARI) {a(n)= local(A); if(n<0, 0, A= x*O(x^n); polcoeff( (1- eta(x+A)^3* 
               eta(x^2+A)^3/ eta(x^3+A)/ eta(x^6+A))/3, n))}
%o A131944 (PARI) {a(n)= local(A, p, e); if(n<1, 0, A=factor(n); prod(k=1, matsize(A)[1], 
               if(p=A[k, 1], e=A[k, 2]; if(p==2, 1, if(p==3, 4-p^(e+1), (p^(e+1)-1)/
               (p-1))))))}
%Y A131944 A131943(n)= -3*a(n) unless n=0.
%Y A131944 Sequence in context: A077491 A086231 A163336 this_sequence A058651 A164105 
               A160824
%Y A131944 Adjacent sequences: A131941 A131942 A131943 this_sequence A131945 A131946 
               A131947
%K A131944 sign
%O A131944 1,3
%A A131944 Michael Somos, Jul 30 2007

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