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A002284
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q-expansion of modular form of weight 12: eta(8 tau)^12 * theta(tau).
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1
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0, 0, 0, 0, 1, 2, 0, 0, 2, 0, 0, 0, -12, -22, 0, 0, -24, 0, 0, 0, 56, 84, 0, 0, 108, 0, 0, 0, -112, -66, 0, 0, -176, 0, 0, 0, 9, -398, 0, 0, -196, 0, 0, 0, 364, 990, 0, 0, 1056, 0, 0, 0, -616, 70, 0, 0, -728, 0, 0, 0, 432, -2354, 0, 0, -1472, 0, 0, 0, -240, 1080, 0, 0, 990, 0, 0, 0
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,6
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COMMENTS
| Euler transform of period 8 sequence [2,-3,2,-1,2,-3,2,-13,...]. - Michael Somos Mar 06 2004
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1004
R. E. Borcherds, A Siegel cusp form of weight 12 ...
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FORMULA
| Expansion of eta(q^2)^5*eta(q^8)^12/(eta(q)eta(q^4))^2 in powers of q. G.f.: x^4(Product_{k>0} (1-x^(2k))^5(1-x^(8k))^12/((1-x^k)(1-x^(4k)))^2). - Michael Somos Mar 06 2004
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MATHEMATICA
| max = 76; f[x_] := x^4*Product[ (1 - x^(2k))^5 (1 - x^(8k))^12/((1 - x^k) (1 - x^(4k)))^2, {k, 1, max}]; CoefficientList[ Series[ f[x], {x, 0, max}], x] (* From Jean-François Alcover, Dec 12 2011, after Michael Somos *)
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PROG
| (PARI) a(n)=if(n<4, 0, n-=4; polcoeff(eta(x^8+x*O(x^n))^12*sum(k=1, sqrtint(n), 2*x^k^2, 1), n)) - Michael Somos Mar 06 2004
(PARI) a(n)=local(X); if(n<4, 0, n-=4; X=x+x*O(x^n); polcoeff(eta(X^2)^5*eta(X^8)^12/eta(X)^2/eta(X^4)^2, n)) - Michael Somos Mar 06 2004
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CROSSREFS
| Sequence in context: A178923 A130209 A109127 * A016424 A108913 A139032
Adjacent sequences: A002281 A002282 A002283 * A002285 A002286 A002287
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KEYWORD
| sign,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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