A096792 Number of partitions of n into distinct parts with odd number of even parts.

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, 111, 128, 148, 170, 195, 224, 256, 292, 334, 380, 432, 491, 557, 630, 713, 805, 908, 1024, 1152, 1295, 1455, 1632, 1829, 2049, 2291, 2560, 2859, 3189, 3554, 3959, 4404

Offset

1,5

Links

Table of n, a(n) for n=1..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 *)

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, A096791.

Sequence in context: A058724 A029021 A261770 * A335746 A015741 A015753

Adjacent sequences: A096789 A096790 A096791 * A096793 A096794 A096795

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