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Search: id:A116494
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| A116494 |
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Expansion of psi(q^5)/psi(q) in powers of q where psi() is a Ramanujan theta function. |
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3
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| 1, -1, 1, -2, 3, -3, 4, -6, 8, -10, 12, -16, 21, -25, 30, -38, 48, -57, 68, -84, 102, -121, 143, -172, 207, -243, 284, -338, 400, -465, 542, -636, 744, -862, 996, -1158, 1344, -1546, 1776, -2050, 2361, -2701, 3088, -3540, 4050, -4613, 5248, -5980, 6808, -7719, 8742, -9916, 11232, -12682
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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Expansion of q^(-1/2)*eta(q)*eta(q^10)^2/(eta(q^2)^2*eta(q^5)) in powers of q.
Euler transform of period 10 sequence [ -1,1,-1,1,0,1,-1,1,-1,0,...].
Given g.f. A(x), then B(x)=x*A(x^2) satisfies 0=f(B(x),B(x^2)) where f(u,v)=(1-u^2)(1-5u^2)v^2 -(u^2-v^2)^2.
Given g.f. A(x), then B(x)=x*A(x^2) satisfies 0=f(B(x),B(x^2),B(x^4)) where f(u,v,w)=v*w*(1-v^2)-u^2*(v+w)^2.
Given g.f. A(x), then B(x)=x*A(x^2) satisfies 0=f(B(x),B(x^2),B(x^3),B(x^6)) where f(u1,u2,u3,u6)=u2*u6*(u1^2-u3^2) -(u2*u3-u1*u6)^2.
G.f.: Product_{k>0} (1-x^k)/(1-x^(5k))*((1-x^(10k))/(1-x^(2k)))^2 = (Sum_{k>0} x^(5(k^2-k)/2))/(Sum_{k>0} x^((k^2-k)/2)).
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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+A)*eta(x^10+A)^2/eta(x^2+A)^2/eta(x^5+A), n))}
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CROSSREFS
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a(n)=(-1)^n*A036026(n).
Sequence in context: A036030 A036022 A036026 this_sequence A036031 A017818 A091275
Adjacent sequences: A116491 A116492 A116493 this_sequence A116495 A116496 A116497
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Feb 18 2006
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