A241090 Number of partitions p of n such that (number of numbers in p having multiplicity > 1) = number of 1s in p.

1, 0, 1, 1, 1, 3, 3, 5, 6, 10, 12, 16, 21, 29, 36, 47, 58, 77, 93, 121, 146, 185, 225, 280, 338, 419, 505, 612, 743, 888, 1075, 1283, 1539, 1822, 2190, 2575, 3073, 3612, 4287, 5022, 5936, 6938, 8158, 9527, 11151, 12983, 15156, 17617, 20468, 23770, 27531

Offset: 0

Author

Clark Kimberling, Apr 24 2014

Keywords

• nonn
• easy

Examples

			a(6) counts these 3 partitions:  6, 42, 2211.
		

Crossrefs

Cf. A241409, A241131.

Programs

Mathematica

z = 30; f[n_] := f[n] = IntegerPartitions[n]; e[p_] := Length[DeleteDuplicates[Select[p, Count[p, #] > 1 &]]]; Table[Count[f[n], p_ /; e[p] == Count[p, 1]], {n, 0, z}]