OFFSET
0,7
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
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