A096792 - OEIS

%I #8 Mar 29 2015 19:38:52

%S 0,1,1,1,2,2,3,3,4,5,6,8,9,11,13,16,19,23,27,32,38,44,52,61,71,82,96,

%T 111,128,148,170,195,224,256,292,334,380,432,491,557,630,713,805,908,

%U 1024,1152,1295,1455,1632,1829,2049,2291,2560,2859,3189,3554,3959,4404

%N Number of partitions of n into distinct parts with odd number of even parts.

%F a(n) = (A000009(n) - (-1)^n*A010815(n))/2.

%t f[n_] := (PartitionsQ[n] + (-1)^(n + 1)* CoefficientList[ Series[ Product[(1 - x^k), {k, 1, 70}], {x, 0, 70}], x][[n + 1]])/2; Table[ f[n], {n, 0, 60}] (* _Robert G. Wilson v_, Aug 27 2004 *)

%o (PARI) a(n)=local(A); if(n<0,0, A=x^n*O(x); polcoeff((eta(x^2+A)/eta(x+A) - eta(-x+A))/2,n)) /* _Michael Somos_, Aug 27 2004 */

%Y Cf. A067659, A067661, A096791.

%K easy,nonn

%O 1,5

%A _Vladeta Jovovic_, Aug 16 2004

%E More terms from _Robert G. Wilson v_ and _Michael Somos_, Aug 27 2004