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A096791
Number of partitions of n into distinct parts with even number of even parts.
1
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
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
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