A096791 Number of partitions of n into distinct parts with even number of even parts.

1, 1, 0, 1, 1, 1, 2, 2, 3, 4, 5, 6, 7, 9, 11, 14, 16, 19, 23, 27, 32, 38, 45, 52, 61, 71, 83, 96, 111, 128, 148, 170, 195, 224, 256, 293, 334, 380, 432, 491, 556, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2048, 2291, 2560, 2859, 3189, 3554, 3958, 4404

Offset

0,7

Links

Table of n, a(n) for n=0..58.

Formula

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

Mathematica

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 *)
Table[Count[Select[IntegerPartitions[n], Length[#]==Length[Union[#]]&], _?(EvenQ[ Length[ Select[#, EvenQ]]]&)], {n, 0, 60}] (* Harvey P. Dale, Mar 14 2023 *)

Prog

(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 */

Crossrefs

Cf. A067659, A067661, A096792.

Sequence in context: A112193 A014215 A067014 * A199122 A086740 A120161

Adjacent sequences: A096788 A096789 A096790 * A096792 A096793 A096794

Keyword

easy,nonn

Author

Vladeta Jovovic, Aug 16 2004

Extensions

More terms from Robert G. Wilson v and Michael Somos, Aug 27 2004

Status

approved