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A164612
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Expansion of q^(-1) * phi^2(q) * chi^3(q^9) / (chi(q^3) * phi^2(q^9)) in powers of q where phi(), chi() are Ramanujan theta functions.
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0
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1, 4, 4, -1, 0, 4, 1, 0, 0, 1, 0, -8, -1, 0, -8, 0, 0, 4, 1, 0, 16, -2, 0, 16, 0, 0, -4, 2, 0, -32, -3, 0, -32, 1, 0, 8, 4, 0, 56, -4, 0, 56, 1, 0, -16, 4, 0, -96, -6, 0, -92, 1, 0, 24, 5, 0, 160, -8, 0, 152, 1, 0, -40, 8, 0, -252, -10, 0, -240, 2, 0, 64, 11, 0, 392, -14, 0, 368, 4, 0, -96, 14, 0, -600, -19, 0, -560, 4, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| -1,2
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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^3)^3 / (q * chi(q)) + 4 + 4 * q * chi(q) / chi(q^3)^3 in powers of q where chi() is a Ramanujan theta function.
Expansion of eta(q^2)^10 * eta(q^3) * eta(q^9) * eta(q^12) * eta(q^36) / (eta(q)^4 * eta(q^4)^4 * eta(q^6)^2 * eta(q^18)^4) in powers of q.
Euler transform of period 36 sequence [ 4, -6, 3, -2, 4, -5, 4, -2, 2, -6, 4, -2, 4, -6, 3, -2, 4, -2, 4, -2, 3, -6, 4, -2, 4, -6, 2, -2, 4, -5, 4, -2, 3, -6, 4, 0, ...].
a(3*n) = 0 unless n=0. A164268(n) = a(n) unless n=0.
Convolution of A164613 and A062244.
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EXAMPLE
| 1/q + 4 + 4*q - q^2 + 4*q^4 + q^5 + q^8 - 8*q^10 - q^11 - 8*q^13 + ...
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PROG
| (PARI) {a(n) = local(A); if( n<-1, 0, n++; A = x * O(x^n); polcoeff( eta(x^2 + A)^10 * eta(x^3 + A) * eta(x^9 + A) * eta(x^12 + A) * eta(x^36 + A) / (eta(x + A)^4 * eta(x^4 + A)^4 * eta(x^6 + A)^2 * eta(x^18 + A)^4), n))}
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CROSSREFS
| Sequence in context: A048152 A070430 A163353 * A180401 A057270 A057278
Adjacent sequences: A164609 A164610 A164611 * A164613 A164614 A164615
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Aug 17 2009
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