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Number of partitions of n into distinct parts with an even rank.
10

%I #8 Oct 06 2021 18:44:20

%S 1,0,2,0,2,2,3,2,4,6,6,7,8,12,14,16,18,24,26,32,38,46,52,60,70,83,96,

%T 112,128,148,170,194,224,256,293,334,380,432,492,556,630,712,804,908,

%U 1026,1152,1296,1454,1632,1828,2048,2292,2560,2858,3190,3554,3959,4404

%N Number of partitions of n into distinct parts with an even rank.

%F a(n) = Sum(A117195(n,k)*(1 - k mod 2): 0<=k<n).

%F a(n) = A117194(n)+A010054(n) = A000009(n)-A117193(n) = A117193(n)+A003406(n).

%t a[n_] := Count[IntegerPartitions[n], q_ /; EvenQ[First[q] - Length[q]] && Length[q] == Length[Union[q]]];

%t Array[a, 60] (* _Jean-François Alcover_, Oct 06 2021 *)

%Y Cf. A000009, A003406, A101709, A101708, A117193, A117194, A117195.

%K nonn

%O 1,3

%A _Reinhard Zumkeller_, Mar 03 2006