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A122830
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Expansion of c(q)c(q^6)/c(q^2)^2 in powers of q where c(q) is a cubic AGM analog function.
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1
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1, 1, 0, -2, -3, 0, 5, 7, 0, -12, -15, 0, 26, 32, 0, -50, -63, 0, 92, 114, 0, -168, -201, 0, 295, 350, 0, -496, -591, 0, 818, 967, 0, -1332, -1554, 0, 2126, 2468, 0, -3324, -3855, 0, 5126, 5916, 0, -7824, -8970, 0, 11793, 13471, 0, -17548, -20007, 0, 25857, 29384, 0, -37788, -42771, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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FORMULA
| Expansion of eta(q^2)^2*eta(q^3)^3*eta(q^18)^3/(eta(q)eta(q^6)^7) in powers of q.
Euler transform of period 18 sequence [ 1, -1, -2, -1, 1, 3, 1, -1, -2, -1, 1, 3, 1, -1, -2, -1, 1, 0, ...].
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=4*v -4*u^2 +4*v^2 +2*w^2 +8*u*v +8*v*w +18*u*v*w +3*u*w^2 -12*u^2*w -12*u^2*v +6*v^2*w -3*v^3 -9*u^2*w^2 -18*u^2*v*w -9*u*v^2*w -9*u^2*v^2 -9*v^3*w.
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^3), A(x^6)) where f(u1, u2, u3, u6)= +2*u6*u1 -2*u3*u2 +u6*u2^2 -3*u6*u3*u2 -3*u3^2*u2 -4*u3*u2^2 -3*u3^2*u2^2 +6*u3^2*u1 -4*u3*u2*u1 +4*u6*u2*u1 +u6*u1^2 +2*u3*u1^2 +6*u3^2*u1^2 +3*u6*u3*u1^2 -6*u6*u3*u2^2 +6*u3^2*u2*u1 -6*u6*u3*u2*u1.
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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)^2*eta(x^3+A)^3*eta(x^18+A)^3/eta(x+A)/eta(x^6+A)^7, n))}
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CROSSREFS
| Sequence in context: A190621 A049268 A004179 * A190902 A115562 A127468
Adjacent sequences: A122827 A122828 A122829 * A122831 A122832 A122833
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KEYWORD
| sign
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AUTHOR
| Michael Somos, Sep 12 2006
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