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A131126
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Expansion of (eta(q^4)^5/( eta(q)^2* eta(q^2)* eta(q^8)^2) )^2 in powers of q.
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2
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1, 4, 16, 48, 128, 312, 704, 1504, 3072, 6036, 11488, 21264, 38400, 67864, 117632, 200352, 335872, 554952, 904784, 1457136, 2320128, 3655296, 5702208, 8813472, 13504512, 20523996, 30952544, 46340832, 68901888, 101777112, 149403264
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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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 (phi(q^2) / phi(-q))^2 in powers of q where phi() is a Ramanujan theta function.
Expansion of ((phi(q) / phi(-q))^2 + 1) / 2 in powers of q where phi() is a Ramanujan theta function.
Euler transform of period 8 sequence [ 4, 6, 4, -4, 4, 6, 4, 0, ...].
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EXAMPLE
| 1 + 4*q + 16*q^2 + 48*q^3 + 128*q^4 + 312*q^5 + 704*q^6 + 1504*q^7 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x + A)^2 * eta(x^2 + A) * eta(x^8 + A)^2 / eta(x^4 + A)^5)^-2, n))}
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CROSSREFS
| 4 * A107035(n) = a(n) unless n=0. A014969(n) = 2 * a(n) unless n=0.
Sequence in context: A100625 A203248 A071009 * A159964 A058922 A034918
Adjacent sequences: A131123 A131124 A131125 * A131127 A131128 A131129
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Jun 15 2007
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