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Search: id:A122854
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| A122854 |
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Expansion of phi(q)^2*psi(q)^4 in powers of q where phi(),psi() are Ramanujan theta functions. |
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+0
3
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| 1, 8, 26, 48, 73, 120, 170, 208, 290, 360, 384, 528, 651, 656, 842, 960, 960, 1248, 1370, 1360, 1682, 1848, 1898, 2208, 2353, 2320, 2810, 3120, 2880, 3480, 3722, 3504, 4420, 4488, 4224, 5040, 5330, 5208, 5760, 6240, 5905, 6888, 7540, 6736, 7922, 8160, 7680
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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Expansion of q^(-1/2)eta(q^2)^18/(eta(q)^8*eta(q^4)^4) in powers of q.
Euler transform of period 4 sequence [ 8, -10, 8, -6, ...].
a(n)=b(2n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(p^e) = ((p^2)^(e+1)-1)/(p^2-1) if p == 1 (mod 4), b(p^e) = ((p^2)^(e+1)-(-1)^(e+1))/(p^2+1) if p == 3 (mod 4).
G.f.: Sum_{k>0 odd} k^2*x^k/(1+x^(2k)) = Product_{k>0} (1-x^(2k))^6*(1+x^k)^8/(1+x^(2k))^4.
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PROGRAM
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(PARI) {a(n)= local(A, p, e, f); if(n<0, 0, n=2*n+1; A=factor(n); prod(k=1, matsize(A)[1], if(p=A[k, 1], e=A[k, 2]; if(p==2, 0, f=(-1)^(p\2); (p^(2*e+2)-f^(e+1))/(p^2-f)))))}
(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^18/(eta(x+A)^8*eta(x^4+A)^4), n))}
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CROSSREFS
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A050458(2n+1)=A050470(2n+1)=a(n).
Sequence in context: A069952 A031085 A031307 this_sequence A138502 A143894 A126176
Adjacent sequences: A122851 A122852 A122853 this_sequence A122855 A122856 A122857
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KEYWORD
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nonn
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AUTHOR
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Michael Somos, Sep 14 2006
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