A007706 a(n) = 1 + coefficient of x^n in Product_{k>=1} (1-x^k) (essentially the expansion of the Dedekind function eta(x)). (Formerly M0013)

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

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, p. 825.

Formula

eta(z) = q^(1/24) Product_{m>=1} (1-q^m), q=exp(2 Pi i z).

G.f.: 1/(1-x) + Product_{k>0} (1-x^k). - Michael Somos, Jun 26 2004

Maple

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

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}] (* Jean-François Alcover, Jan 06 2012 *)
1 + CoefficientList[QPochhammer[q] + O[q]^120, q] (* Jean-François Alcover, Nov 24 2015 *)

Prog

(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: A039977 A197548 A029403 * A241069 A261084 A035144

Adjacent sequences: A007703 A007704 A007705 * A007707 A007708 A007709

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Sep 19 1994

Status

approved