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Number of partitions of n not containing the number of distinct parts as a part.
2

%I #4 Apr 03 2014 03:40:22

%S 1,0,1,1,3,3,6,8,12,16,23,32,42,58,74,102,131,170,220,283,359,462,579,

%T 727,922,1136,1424,1763,2183,2667,3308,4019,4917,5982,7285,8774,10666,

%U 12797,15437,18505,22181,26481,31678,37649,44773,53177,62994,74466,88014

%N Number of partitions of n not containing the number of distinct parts as a part.

%F a(n) + A239945(n) = A000041(n) for n >= 0.

%e a(7) counts these 8 partitions: 7, 61, 511, 43, 421, 4111, 331, 31111.

%t z = 55; d[p_] := d[p] = Length[DeleteDuplicates[p]]; Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, d[p]]], {n, 0, z}] (* A239945 *)

%t Table[PartitionsP[n] - t[[n + 1]], {n, 0, z}] (* A239946 *)

%Y Cf. A239945.

%K nonn,easy

%O 0,5

%A _Clark Kimberling_, Mar 30 2014