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A007706
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1 + coefficient of x^n in Product (1-x^k ), k=1.. inf (essentially the expansion of the Dedekind function eta(x)).
(Formerly M0013)
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3
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2, 0, 0, 1, 1, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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REFERENCES
| M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 825.
B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 70.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..1000
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].
M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 825.
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FORMULA
| eta(z) = q^(1/24) Product( 1-q^m, m=1..inf), q=exp(2 Pi i z).
G.f.: 1/(1-x)+Prod_{k>0}(1-x^k). - Michael Somos Jun 26 2004
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MAPLE
| eta := q^(1/24)*mul( (1-q^m), m=1..100);
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MATHEMATICA
| p[n_] := p[n] = Expand[p[n-1]*(1-x^n)]; p[1] = 1-x; a[n_] := 1+Coefficient[p[n], x^n]; a[0] = 2; Table[a[n], {n, 0, 104}](* From Jean-François Alcover, Jan 06 2012 *)
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PROG
| (PARI) a(n)=if(n<0, 0, 1+polcoeff(eta(x+x*O(x^n)), n)) /* Michael Somos Jun 26 2004 */
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CROSSREFS
| Cf. A010815.
Sequence in context: A039977 A197548 A029403 * A035144 A157045 A035208
Adjacent sequences: A007703 A007704 A007705 * A007707 A007708 A007709
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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