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Search: id:A030210
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| A030210 |
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Expansion of (eta(q)*eta(q^5))^4. |
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+0
1
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| 1, -4, 2, 8, -5, -8, 6, 0, -23, 20, 32, 16, -38, -24, -10, -64, 26, 92, 100, -40, 12, -128, -78, 0, 25, 152, -100, 48, -50, 40, -108, 256, 64, -104, -30, -184, 266, -400, -76, 0, 22, -48, 442, 256, 115, 312, -514, -128, -307, -100, 52, -304, 2, 400, -160, 0, 200, 200, 500, -80, -518, 432, -138, -512
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Conjecture: |a(p)| < 2*p^(3/2) for p prime. - Michael Somos Oct 31 2005
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REFERENCES
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M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
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FORMULA
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Euler transform of period 5 sequence [ -4, -4, -4, -4, -8, ...]. - Michael Somos, May 02 2005
G.f. A(x) satisfies 0=f(A(x), A(x^2), A(x^4)) where f(u, v, w)=-v^3+8uvw+16uw^2+u^2w. - Michael Somos May 02 2005
a(n) is multiplicative and a(5^e) = (-5)^e, a(p^(e+2)) = a(p)a(p^(e+1))-p^3*a(p^e).
G.f.: x (Product_{k>0} (1-x^k)(1-x^(5k)))^4.
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PROGRAM
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(PARI) {a(n)=local(A); if(n<1, 0, n--; A=x^n*O(x); polcoeff( (eta(x+A)*eta(x^5+A))^4, n))}
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CROSSREFS
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Sequence in context: A030181 A021879 A020806 this_sequence A098798 A131783 A094312
Adjacent sequences: A030207 A030208 A030209 this_sequence A030211 A030212 A030213
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KEYWORD
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sign,mult
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AUTHOR
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njas
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