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Number of partitions of n into distinct parts with an odd rank.
12

%I #8 Oct 06 2021 18:43:34

%S 0,1,0,2,1,2,2,4,4,4,6,8,10,10,13,16,20,22,28,32,38,43,52,62,72,82,96,

%T 110,128,148,170,196,224,256,292,334,380,432,490,557,630,714,806,908,

%U 1022,1152,1294,1456,1632,1830,2049,2290,2560,2860,3188,3554,3958,4404

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

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

%F a(n) = A000009(n) - A117192(n).

%F a(n) = A117192(n) - A003406(n).

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

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

%Y Cf. A000009, A003406, A101707, A117192.

%K nonn

%O 1,4

%A _Reinhard Zumkeller_, Mar 03 2006