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

%I A007706 M0013 #35 Aug 28 2016 18:23:35
%S A007706 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,
%T A007706 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,
%U A007706 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
%N A007706 a(n) = 1 + coefficient of x^n in Product_{k>=1} (1-x^k) (essentially the expansion of the Dedekind function eta(x)).
%D A007706 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 825.
%D A007706 B. Schoeneberg, Elliptic Modular Functions, Springer-Verlag, NY, 1974, p. 70.
%D A007706 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007706 T. D. Noe, <a href="/A007706/b007706.txt">Table of n, a(n) for n = 0..1000</a>
%H A007706 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.convertit.com/Go/ConvertIt/Reference/AMS55.ASP">Handbook of Mathematical Functions</a>, National Bureau of Standards Applied Math. Series 55, Tenth Printing, 1972, p. 825.
%F A007706 eta(z) = q^(1/24) Product_{m>=1} (1-q^m), q=exp(2 Pi i z).
%F A007706 G.f.: 1/(1-x) + Product_{k>0} (1-x^k). - _Michael Somos_, Jun 26 2004
%p A007706 eta := q^(1/24)*mul( (1-q^m), m=1..100);
%t A007706 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 *)
%t A007706 1 + CoefficientList[QPochhammer[q] + O[q]^120, q] (* _Jean-François Alcover_, Nov 24 2015 *)
%o A007706 (PARI) a(n)=if(n<0,0,1+polcoeff(eta(x+x*O(x^n)),n)) /* _Michael Somos_, Jun 26 2004 */
%Y A007706 Cf. A010815.
%K A007706 nonn,easy,nice
%O A007706 0,1
%A A007706 _N. J. A. Sloane_, Sep 19 1994