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A007706 1 + coefficient of x^n in Product (1-x^k ), k=1.. inf (essentially the expansion of the Dedekind function eta(x)).
(Formerly M0013)
+0
3
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; listen)
OFFSET

0,1

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).

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.

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

MAPLE

eta := q^(1/24)*mul( (1-q^m), m=1..100);

PROGRAM

(PARI) a(n)=if(n<0, 0, 1+polcoeff(eta(x+x*O(x^n)), n)) /* Michael Somos Jun 26 2004 */

CROSSREFS

Cf. A010815.

Sequence in context: A052154 A039977 A029403 this_sequence A035144 A157045 A035208

Adjacent sequences: A007703 A007704 A007705 this_sequence A007707 A007708 A007709

KEYWORD

nonn,easy,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

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Last modified December 10 12:37 EST 2009. Contains 170569 sequences.


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