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Search: id:A131124
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| A131124 |
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Expansion of (q^-1)* (phi(-q)/ psi(q^4))^2 in powers of q where phi(), psi() are Ramanujan theta functions. |
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+0
2
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| 1, -4, 4, 0, 2, 0, -8, 0, -1, 0, 20, 0, -2, 0, -40, 0, 3, 0, 72, 0, 2, 0, -128, 0, -4, 0, 220, 0, -4, 0, -360, 0, 5, 0, 576, 0, 8, 0, -904, 0, -8, 0, 1384, 0, -10, 0, -2088, 0, 11, 0, 3108, 0, 12, 0, -4552, 0, -15, 0, 6592, 0, -18, 0, -9448, 0, 22, 0, 13392, 0, 26, 0, -18816, 0, -29, 0, 26216, 0, -34, 0
(list; graph; listen)
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OFFSET
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-1,2
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FORMULA
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Expansion of (eta(q)^2* eta(q^4)/( eta(q^2)* eta(q^8)^2 ))^2 in powers of q.
Euler transform of period 8 sequence [ -4, -2, -4, -4, -4, -2, -4, 0, ...].
G.f. is a Fourier series which satisfies f(-1/(8 t)) = 32/ f(t) where q= exp(2 pi i t).
G.f. A(x) satisfies 0= f(A(x), A(x^2)) where f(u, v)= u* (u+8) *(v+4) -v^2.
G.f.: (1/x)* (Product_{k>0} (1+x^k)^4* (1+x^(2*k))^2* (1+x^(4*k))^4)^-1.
a(2n)=0 if n>0.
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EXAMPLE
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1/q - 4 + 4*q +2*q^3 - 8*q^5 - q^7 + 20*q^9 - 2*q^11 - 40*q^13 + 3*q^15 + ...
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PROGRAM
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(PARI) {a(n)= local(A); if(n<-1, 0, n++; A= x*O(x^n); polcoeff( (eta(x+A)^2 *eta(x^4+A)/ eta(x^2+A)/ eta(x^8+A)^2 )^2, n))}
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CROSSREFS
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A029841(n)= a(n) unless n=0. A029839(n) = a(4n-1). A079006(n) = a(4n+1)/4.
Convolution inverse of A107035.
Sequence in context: A067007 A066298 A108068 this_sequence A131125 A106508 A104287
Adjacent sequences: A131121 A131122 A131123 this_sequence A131125 A131126 A131127
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Jun 15 2007
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