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A123758
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Expansion of q^(-1/3)eta(q)eta(q^4)eta(q^5)/eta(q^2) in powers of q.
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0
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1, -1, 0, -1, 0, -1, 2, 0, 1, 0, 0, 0, 0, 1, 0, -2, -1, 0, 0, 0, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, -1, 0, 2, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 1, 0, 0, -1, 0, 0, 0, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, -1, 0, -1, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,7
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COMMENTS
| Ramanujan theta functions: f(q) := Prod_{k>=1} (1-(-q)^k) (see A121373), phi(q) := theta_3(q) := Sum_{k=-oo..oo} q^(k^2) (A000122), psi(q) := Sum_{k=0..oo} q^(k*(k+1)/2) (A10054), chi(q) := Prod_{k>=0} (1+q^(2k+1)) (A000700).
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LINKS
| M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of f(-q^5)*psi(-q) in powers of q where f(),psi() are Ramanujan theta functions.
Euler transform of period 20 sequence [ -1, 0, -1, -1, -2, 0, -1, -1, -1, -1, -1, -1, -1, 0, -2, -1, -1, 0, -1, -2, ...].
Product_{k>0} (1-x^k)*(1+x^(2k))*(1-x^(5k)).
a(8n+2) = a(8n+4) = 0.
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PROG
| (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( eta(x+A)*eta(x^4+A)*eta(x^5+A)/eta(x^2+A), n))}
(PARI) {a(n) = local(s, k); if(n<0, 0, n=24*n+8; for(j=1, sqrtint(n\5), if((j^2%6==1)& issquare( (n-5*j^2)/3, &k)& (k%2), s+= (-1)^((j+1)\6+ (k+2)\4))); s)}
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CROSSREFS
| Sequence in context: A045827 A070103 A113048 * A069846 A161520 A070097
Adjacent sequences: A123755 A123756 A123757 * A123759 A123760 A123761
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Oct 12 2006
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