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Search: id:A030211
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| A030211 |
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Expansion of q^(-1/2)(eta(q)eta(q^2))^4 in powers of q. |
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+0
2
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| 1, -4, -2, 24, -11, -44, 22, 8, 50, 44, -96, -56, -121, 152, 198, -160, 176, -48, -162, -88, -198, 52, 22, 528, 233, -200, -242, 88, -176, -668, 550, -264, -44, 188, 224, 728, 154, 484, -1056, -656, -311, 236, -100, -792, 714, 528, 640, -88, -478, 484, 1566, -968, 192, -780, -1994, 648, -942
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Euler transform of period 2 sequence [ -4,-8,...]. - Michael Somos Apr 14 2004
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REFERENCES
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M. Koike, On McKay's conjecture, Nagoya Math. J., 95 (1984), 85-89.
M. Boylan, Exceptional congruences for the coefficients of certain eta-product newforms, J. Number Theory 98 (2003), no. 2, 377-389. p. 378. MR1955423 (2003k:11071)
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LINKS
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Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
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FORMULA
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G.f.: (Product_{k>0} (1-x^k)(1-x^(2k)))^4.
Given g.f. A(x), then B(x)=x*A(x^2) satisfies 0=f(B(x), B(x^2), B(x^3), B(x^6)) where f(u1,u2,u3,u6)=(81*u6*u3+u1*u2)*(u2*u3+u1*u6) +30*u1*u2*u3*u6 -256*u2^2*u6^2 -5*u2^2*u3^2 -5*u1^2*u6^2 -u1^2*u3^2 . - Michael Somos Mar 08 2006
Given A=A0+A1+A2+A3 is the 4-section, then 0=8*A0*A2*(A0^2+A2^2) +(A1^2-A3^2)*(A0^2-A2^2) . - Michael Somos Mar 08 2006
a(n)=b(2n+1) where b(n) is multiplicative and b(2^e) = 0^e, b(p^e) = b(p)*b(p^(e-1)) -p^3*b(p^(e-2)) . - Michael Somos Mar 08 2006
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff((eta(x+x*O(x^n))*eta(x^2+x*O(x^n)))^4, n)) /* Michael Somos Apr 14 2004 */
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CROSSREFS
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Sequence in context: A016517 A157407 A100400 this_sequence A134461 A058167 A140331
Adjacent sequences: A030208 A030209 A030210 this_sequence A030212 A030213 A030214
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KEYWORD
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sign
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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