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

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

Author

N. J. A. Sloane, Sep 19 1994

Keywords

• nonn
• easy
• nice

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.

Crossrefs

Cf. A010815.

Programs

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 *)

PARI

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

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