%I A067661
%S A067661 1,0,0,1,1,2,2,3,3,4,5,6,7,9,11,13,16,19,23,27,32,38,45,52,61,71,83,96,
%T A067661 111,128,148,170,195,224,256,292,334,380,432,491,556,630,713,805,908,
%U A067661 1024,1152,1295,1455,1632,1829,2049,2291,2560,2859,3189,3554,3959,4404
%N A067661 Number of partitions of n into distinct parts such that number of parts 
               is an even number.
%D A067661 B. C. Berndt, Ramanujan's Notebooks Part III, Springer-Verlag, see p. 
               18 Entry 9 Corollary (2).
%F A067661 G.f.: A(q) = Sum_{n >= 0} a(n) q^n = 1 + q^3 + q^4 + 2 q^5 + 2 q^6 + 
               3 q^7 + ... = Sum_{n >= 0} q^(n(2n+1))/(q; q)_{2n} (R. William Gosper 
               (rwg(AT)osots.com), Jun 25 2005)
%F A067661 Also, let B(q) = Sum_{n >= 0} A067659(n) q^n = q + q^2 + q^3 + q^4 + 
               q^5 + 2 q^6 + ... Then B(q) = Sum_{n >= 0} q^((n+1)(2n+1))/(q; q)_{2n+1}.
%F A067661 Also we have the following identity involving 2 X 2 matrices:
%F A067661 Prod_{k >= 1} [ 1 q^k / q^k 1 ] = [ A(q) B(q) / B(q) A(q) ] (R. William 
               Gosper (rwg(AT)osots.com), Jun 25 2005)
%F A067661 a(n) = (A000009(n)+A010815(n))/2. - Vladeta Jovovic (vladeta(AT)eunet.rs), 
               Feb 24 2002
%F A067661 Expansion of (1+phi(-q))/(2*chi(-q)) in powers of q where phi(),chi() 
               are Ramanujan theta functions. - Michael Somos Feb 14 2006
%o A067661 (PARI) {a(n)=local(A); if(n<0, 0, A=x*O(x^n); polcoeff( (eta(x^2+A)/eta(x+A)+eta(x+A))/
               2, n))} /* Michael Somos Feb 14 2006 */
%Y A067661 Sequence in context: A036821 A026798 A125890 this_sequence A052839 A125894 
               A091493
%Y A067661 Adjacent sequences: A067658 A067659 A067660 this_sequence A067662 A067663 
               A067664
%K A067661 easy,nonn
%O A067661 0,6
%A A067661 Naohiro Nomoto (n_nomoto(AT)yabumi.com), Feb 23 2002