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A106508
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Expansion of psi(x)^4 * chi(-x^2)^2 in powers of x where psi(), chi() are Ramanujan theta functions.
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1, 4, 4, 0, 2, 0, -8, 0, -5, -16, 4, 0, -10, 0, -8, 0, 9, 8, 0, 0, 14, 0, 16, 0, -10, 32, 4, 0, 0, 0, 8, 0, 14, -20, -20, 0, 2, 0, 0, 0, -11, -16, -20, 0, -32, 0, 16, 0, 0, -40, 4, 0, 14, 0, -8, 0, -9, 32, -20, 0, 26, 0, 0, 0, 2, 36, 28, 0, 0, 0, 16, 0, 16, 0, 28, 0, -22, 0, 0, 0, 14, 56, -16, 0, 0, 0, -40, 0, 0
(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
| C. Adiga, N. Anitha and T. Kim, Transformations of Ramanujan's Summation Formula and its Applications, See page 5
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
| Expansion of q^(-1/3) * eta(q^2)^10 / (eta(q)^4 * eta(q^4)^2) in powers of q.
Euler transform of period 4 sequence [4, -6, 4, -4, ...].
a(n) = (-1)^n * A187149(n). a(4*n + 3) = a(8*n + 5) = 0.
G.f. Product_{k>0} (1 + x^k)^4 (1 - x^(2*k))^4 / (1 + x^(2*k))^2.
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EXAMPLE
| 1 + 4*x + 4*x^2 + 2*x^4 - 8*x^6 - 5*x^8 - 16*x^9 + 4*x^10 - 10*x^12 + ...
q + 4*q^4 + 4*q^7 + 2*q^13 - 8*q^19 - 5*q^25 - 16*q^28 + 4*q^31 - 10*q^37 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<0, 0, A = x * O(x^n); polcoeff( eta(x^2 + A)^10 / (eta(x^4 + A)^2 * eta(x + A)^4), n))}
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CROSSREFS
| Cf. A187149.
Sequence in context: A131124 A131125 A187149 * A177036 A158100 A104287
Adjacent sequences: A106505 A106506 A106507 * A106509 A106510 A106511
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KEYWORD
| sign
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AUTHOR
| Michael Somos, May 24 2005
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