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A134004
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Expansion of (chi(-q) * chi(-q^19))^(-2) in powers of q where chi() is a Ramanujan theta function.
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1
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1, 2, 3, 6, 9, 14, 22, 32, 46, 66, 93, 128, 176, 238, 319, 426, 562, 736, 960, 1244, 1602, 2054, 2620, 3324, 4203, 5292, 6634, 8290, 10322, 12808, 15845, 19542, 24028, 29468, 36042, 43966, 53506, 64960, 78685, 95106, 114709, 138066, 165855, 198856, 237979
(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 q^(-5/3) * (eta(q^2) * eta(q^38) / ( eta(q) * eta(q^19) ))^2 in powers of q.
Euler transform of period 38 sequence [ 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, 2, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (342 t)) = (1/4) / f(t) where q = exp(2 pi i t).
G.f.: (Product_{k>0} (1 + x^k) * (1 + x^(19*k)))^2.
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EXAMPLE
| q^5 + 2*q^8 + 3*q^11 + 6*q^14 + 9*q^17 + 14*q^20 + 22*q^23 + 32*q^26 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A) * eta(x^38 + A) / eta(x + A) / eta(x^19 + A))^2, n))}
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CROSSREFS
| Convolution inverse of A134005.
Sequence in context: A058609 A128518 A022567 * A123631 A018060 A115856
Adjacent sequences: A134001 A134002 A134003 * A134005 A134006 A134007
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Oct 01 2007
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