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Search: id:A001934
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| A001934 |
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Expansion of 1/theta_4(q)^2 in powers of q.
(Formerly M3443 N1397)
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+0
3
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| 1, 4, 12, 32, 76, 168, 352, 704, 1356, 2532, 4600, 8160, 14176, 24168, 40512, 66880, 108876, 174984, 277932, 436640, 679032, 1046016, 1597088, 2418240, 3632992, 5417708, 8022840, 11802176, 17252928, 25070568, 36223424, 52053760, 74414412
(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 [4,2,...].
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
A. Cayley, A memoir on the transformation of elliptic functions, Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 9, p. 128.
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FORMULA
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G.f.: Product ( 1 - x^k )^{-c(k)}, c(k) = 4, 2, 4, 2, 4, 2, ....
G.f. prod{i=1, oo, (1+x^i)^2}/prod{i=1, oo, (1-x^i)^2} - Jon Perry (perry(AT)globalnet.co.uk), Apr 04 2004
Expansion of eta(q^2)^2/eta(q)^4 in powers of q.
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PROGRAM
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(PARI) y=prod(i=1, 20, (1+x^i)^2)/prod(i=1, 20, (1-x^i)^2); for(i=0, 20, print1(", "polcoeff(y, i)))
(PARI) a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^2/eta(x+A)^4, n)) /* Michael Somos Feb 09 2006 */
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CROSSREFS
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Apart from signs, same as A004403.
Equals 4 * A002318(n), n>0.
Sequence in context: A133212 A127811 A138517 this_sequence A004403 A084566 A079769
Adjacent sequences: A001931 A001932 A001933 this_sequence A001935 A001936 A001937
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Sep 08 2000
Edited by N. J. A. Sloane (njas(AT)research.att.com) May 13 2008 to remove an incorrect g.f.
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