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Search: id:A002284
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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; listen)
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OFFSET
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0,6
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COMMENT
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Euler transform of period 8 sequence [2,-3,2,-1,2,-3,2,-13,...]. - Michael Somos Mar 06 2004
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LINKS
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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
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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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PROGRAM
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(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
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Sequence in context: A108498 A130209 A109127 this_sequence A016424 A108913 A139032
Adjacent sequences: A002281 A002282 A002283 this_sequence A002285 A002286 A002287
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KEYWORD
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sign,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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