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Search: id:A123759
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| A123759 |
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Expansion of f(-q)*psi(-q^5) in powers of q where f(), psi() are Ramanujan theta functions. |
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+0
1
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| 1, -1, -1, 0, 0, 0, 1, 2, 0, 0, -1, 0, -2, 0, 0, -2, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, -2, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 2, 0, 0, 0, 0, -2, 0, 0, -2, -1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 2, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0
(list; graph; listen)
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OFFSET
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0,8
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FORMULA
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Euler transform of period 20 sequence [ -1, -1, -1, -1, -2, -1, -1, -1, -1, -1, -1, -1, -1, -1, -2, -1, -1, -1, -1, -2, ...].
Product_{k>0} (1-x^k)*(1-x^(5k))*(1+x^(10k)).
a(8n+3) = a(8n+5) = 0.
Expansion of q^(-2/3) * eta(q) * eta(q^5) * eta(q^20)/ eta(q^10) in powers of q.
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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^5+A)*eta(x^20+A)/eta(x^10+A), n))}
(PARI) {a(n) = local(s, k); if(n<0, 0, n=24*n+16; forstep(k=1, sqrtint(n\15), 2, if(issquare(n-15*k^2, &j)& (j^2%6==1), s+= (-1)^((j+1)\6+ (k+2)\4))); s)}
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CROSSREFS
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Sequence in context: A084888 A091400 A129448 this_sequence A072453 A007423 A076544
Adjacent sequences: A123756 A123757 A123758 this_sequence A123760 A123761 A123762
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Oct 12 2006
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