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A138503
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Expansion of (1 - (eta(q)^2 / eta(q^2))^8) / 16 in powers of q.
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2
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1, -7, 28, -71, 126, -196, 344, -583, 757, -882, 1332, -1988, 2198, -2408, 3528, -4679, 4914, -5299, 6860, -8946, 9632, -9324, 12168, -16324, 15751, -15386, 20440, -24424, 24390, -24696, 29792, -37447, 37296, -34398, 43344, -53747, 50654, -48020, 61544, -73458, 68922
(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 (1 - phi(-q)^8) / 16 in powers of q where phi() is a Ramanujan theta function.
a(n) is multiplicative with a(2^e) = -(8^(e+1) - 15) / 7, a(p^e) = ((p^3)^(e+1) - 1) / (p^3 - 1).
G.f.: Sum_{k>0} k^3 * -(-x)^k / (1 - x^k).
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EXAMPLE
| q - 7*q^2 + 28*q^3 - 71*q^4 + 126*q^5 - 196*q^6 + 344*q^7 - 583*q^8 + ...
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PROG
| (PARI) {a(n) = if( n<0, 0, sumdiv(n, d, -(-1)^d * d^3))}
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CROSSREFS
| -(-1)^n * A008457(n) = a(n). A035016(n) = -16 * a(n) unless n=0.
Sequence in context: A033582 A176362 A008457 * A064951 A073995 A061968
Adjacent sequences: A138500 A138501 A138502 * A138504 A138505 A138506
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KEYWORD
| sign,mult
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AUTHOR
| Michael Somos, Mar 21 2008
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