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Search: id:A002512
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| A002512 |
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Expansion of a modular function.
(Formerly M1380 N0539)
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+0
1
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| 1, 2, 5, 10, 22, 40, 75, 130, 230, 382, 636, 1022, 1645, 2570, 4002, 6110, 9297, 13910, 20715, 30462, 44597, 64584, 93085, 132990, 189164, 266992, 375192, 523800, 728285, 1006684, 1386043, 1898586, 2591120, 3519840, 4764736, 6423032
(list; graph; listen)
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OFFSET
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0,2
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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).
Newman, Morris; Construction and application of a class of modular functions. II. Proc. London Math. Soc. (3) 9 1959 373-387.
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FORMULA
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G.f.: Product ( 1 - x^k )^(-c(k)); c(k) = 2, 2, 2, 4, 2, 2, 2, 4, ....
Expansion of q^(5/12)/(eta(q)eta(q^4))^2 in powers of q.
Euler transform of period 4 sequence [2, 2, 2, 4, ...]. - Michael Somos Nov 10 2005
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PROGRAM
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(PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x+A)*eta(x^4+A))^-2, n))} /* Michael Somos Nov 10 2005 */
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CROSSREFS
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Sequence in context: A110744 A079342 A034456 this_sequence A097096 A073777 A026633
Adjacent sequences: A002509 A002510 A002511 this_sequence A002513 A002514 A002515
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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), Simon Plouffe (simon.plouffe(AT)gmail.com)
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