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A182038
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Expansion of eta(q) * eta(q^36) / (eta(q^4) * eta(q^9)) in powers of q.
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1
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1, -1, -1, 0, 1, 0, -1, 1, 2, 0, -3, 0, 2, 0, -3, 0, 5, 0, -4, -2, 4, 0, -5, 0, 7, 2, -7, 0, 5, 0, -10, 1, 12, 0, -10, 0, 14, -4, -17, 0, 21, 0, -22, 4, 24, 0, -34, 0, 33, 1, -36, 0, 45, 0, -45, -8, 52, 0, -55, 0, 62, 8, -71, 0, 70, 0, -88, 2, 96, 0, -98, 0
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OFFSET
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1,9
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LINKS
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Table of n, a(n) for n=1..72.
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FORMULA
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Euler transform of period 36 sequence [ -1, -1, -1, 0, -1, -1, -1, 0, 0, -1, -1, 0, -1, -1, -1, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, -1, 0, 0, -1, -1, -1, 0, -1, -1, -1, 0, ...].
G.f. is a period 1 Fourier series which satisfies f(-1 / (36 t)) = f(t) where q = exp(2 pi i t).
G.f.: Product_{k>0} (1 - x^k) * (1 - x^(36*k)) / ((1 - x^(4*k)) * (1 - x^9*k)).
a(6*n) = a(6*n + 4) = 0. a(6*n + 2) = -A092848(n). Convolution inverse of A187020.
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EXAMPLE
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q - q^2 - q^3 + q^5 - q^7 + q^8 + 2*q^9 - 3*q^11 + 2*q^13 - 3*q^15 + ...
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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 + A) * eta(x^36 + A) / (eta(x^4 + A) * eta(x^9 + A)), n))}
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CROSSREFS
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Cf. A092848, A187020.
Sequence in context: A163496 A092241 A213266 * A128144 A128145 A128143
Adjacent sequences: A182035 A182036 A182037 * A182039 A182040 A182041
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KEYWORD
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sign
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AUTHOR
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Michael Somos, Apr 07 2012
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STATUS
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approved
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