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Search: id:A128765
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| A128765 |
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Expansion of psi(q)* psi(q^10)/( psi(q^2)* psi(q^5)) in powers of q where psi() is a Ranaujan theta function. |
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+0
1
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| 1, 1, -1, 0, 1, -1, -2, 0, 2, 0, 0, 2, 1, -1, -2, -2, 0, 1, -2, 0, 6, 3, -5, -2, 5, -3, -10, 2, 8, -1, -2, 6, 6, -2, -8, -6, 2, 2, -8, -2, 21, 11, -18, -4, 18, -11, -32, 4, 26, -1, -10, 18, 20, -8, -26, -18, 10, 8, -26, -2, 61, 27, -53, -12, 52, -26, -88, 12, 74, -6, -32, 42, 58, -17, -74, -40, 34, 16, -74, -8, 156, 66, -136, -26
(list; graph; listen)
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OFFSET
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0,7
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FORMULA
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Euler transform of period 20 sequence [ 1, -2, 1, 0, 0, -2, 1, 0, 1, 0, 1, 0, 1, -2, 0, 0, 1, -2, 1, 0, ...].
Given g.f. A(x), then B(x)= x*A(x^2) satisfies 0= f(B(x), B(x^3)) where f(u, v)= (u-v^3)* (u^3-v) -3*u*v* (u-v)^2.
G.f.: Product_{k>0} (1+x^k)* (1+x^(10k))^2/( (1+x^(2k))^2* (1+x^(5k)) ).
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EXAMPLE
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q + q^3 - q^5 + q^9 - q^11 - 2*q^13 + 2*q^17 + 2*q^23 + q^25 - q^27 -...
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PROGRAM
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(PARI) {a(n)= local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x^2+A)^3* eta(x^5+A)* eta(x^20+A)^2/ (eta(x+A)* eta(x^4+A)^2* eta(x^10+A)^3), n))}
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CROSSREFS
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Sequence in context: A101673 A091395 A035220 this_sequence A058087 A073274 A071957
Adjacent sequences: A128762 A128763 A128764 this_sequence A128766 A128767 A128768
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Mar 25 2007
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