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A164269
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Expansion of q * f(q^9)^3 * phi(q) / (f(q^3) * phi(q^3)^3) in powers of q where f(), phi() are Ramanujan theta functions.
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2
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1, 2, 0, -7, -12, 0, 32, 50, 0, -114, -168, 0, 350, 496, 0, -967, -1332, 0, 2468, 3324, 0, -5916, -7824, 0, 13471, 17548, 0, -29384, -37788, 0, 61784, 78578, 0, -125838, -158496, 0, 249230, 311224, 0, -481506, -596676, 0, 909788, 1119624, 0, -1684824, -2060448, 0
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OFFSET
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1,2
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COMMENTS
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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
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Table of n, a(n) for n=1..48.
M. Somos, Introduction to Ramanujan theta functions
Eric Weisstein's World of Mathematics, Ramanujan Theta Functions
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FORMULA
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Euler transform of period 36 sequence [ 2, -3, -5, -1, 2, 8, 2, -1, -2, -3, 2, 3, 2, -3, -5, -1, 2, 2, 2, -1, -5, -3, 2, 3, 2, -3, -2, -1, 2, 8, 2, -1, -5, -3, 2, 0, ...].
a(3*n) = 0.
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EXAMPLE
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q + 2*q^2 - 7*q^4 - 12*q^5 + 32*q^7 + 50*q^8 - 114*q^10 - 168*q^11 + ...
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PROG
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(PARI) {a(n) = local(A); if( n<1, 0, n--; A = x * O(x^n); polcoeff( eta(x^2 + A)^5 * eta(x^3 + A)^7 * eta(x^12 + A)^7 * eta(x^18 + A)^9 / (eta(x + A)^2 * eta(x^4 + A)^2 * eta(x^6 + A)^18 * eta(x^9 + A)^3 * eta(x^36 + A)^3), n))}
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CROSSREFS
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Cf. A164270(n) = a(3*n + 1). 2 * A164271(n) = a(3*n + 2).
Cf. Convolution inverse of A164268.
Sequence in context: A021485 A019821 A016631 * A121814 A195298 A010581
Adjacent sequences: A164266 A164267 A164268 * A164270 A164271 A164272
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Aug 11 2009
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STATUS
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approved
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