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Search: id:A002318
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| A002318 |
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Expansion of (1/theta_4(q)^2 -1)/4 in powers of q.
(Formerly M2736 N1098)
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+0
2
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| 1, 3, 8, 19, 42, 88, 176, 339, 633, 1150, 2040, 3544, 6042, 10128, 16720, 27219, 43746, 69483, 109160, 169758, 261504, 399272, 604560, 908248, 1354427, 2005710, 2950544, 4313232, 6267642, 9055856, 13013440, 18603603, 26463168, 37464230
(list; graph; listen)
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OFFSET
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1,2
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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).
J. W. L. Glaisher, "On the Coefficients in the q-series for pi/2K and 2G/pi", Quart J. Pure and Applied Math., 21 (1885), 60-76.
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FORMULA
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Expansion of (eta(q^2)^2/eta(q)^4 -1)/4 in powers of q.
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MAPLE
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seq(coeff(convert(series(mul(( 1 - x^k )^(-(2+(k mod 2)*2)), k=1..100), x, 100), polynom), x, i)/4, i=1..50); (Pab Ter)
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PROGRAM
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(PARI) a(n)=local(A); if(n<1, 0, A=x*O(x^n); polcoeff(eta(x^2+A)^2/eta(x+A)^4, n)/4) /* Michael Somos Feb 09 2006 */
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CROSSREFS
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Equals (1/4) * A001934(n).
Adjacent sequences: A002315 A002316 A002317 this_sequence A002319 A002320 A002321
Sequence in context: A089924 A072916 A074839 this_sequence A095681 A079583 A099050
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Pab Ter (pabrlos2(AT)yahoo.com), Oct 18 2005
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