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A143895
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Expansion of q^(1/4) * (eta(q^2)^9 / (eta(q)^5 * eta(q^4)^4))^2 in powers of q.
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1
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1, 10, 47, 150, 403, 1002, 2316, 5004, 10309, 20456, 39240, 73102, 132779, 235868, 410785, 702630, 1182342, 1960418, 3206675, 5179670, 8270086, 13062994, 20427293, 31644200, 48589970, 73994118, 111802523, 167685238, 249745021, 369499928
(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 (chi(q)^4 / chi(-q))^2 in powers of q where chi() is a Ramanujan theta function.
Euler transform of period 4 sequence [ 10, -8, 10, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1/(16 t)) = (1/2) g(t) where q = exp(2 pi i t) and g() is g.f. for A143894.
G.f.: (Product_{k>0} (1 + x^k)^5 / (1 + x^(2*k))^4)^2.
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EXAMPLE
| q^-1 + 10*q^3 + 47*q^7 + 150*q^11 + 403*q^15 + 1002*q^19 + 2316*q^23 + ...
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PROG
| (PARI) {a(n) = if( n<0, 0, A = x * O(x^n); polcoeff( (eta(x^2 + A)^9 / (eta(x + A)^5 * eta(x^4 + A)^4))^2, n))}
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CROSSREFS
| Sequence in context: A003765 A138041 A000832 * A034443 A121075 A121073
Adjacent sequences: A143892 A143893 A143894 * A143896 A143897 A143898
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KEYWORD
| nonn
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AUTHOR
| Michael Somos, Sep 04 2008
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