A240076 Number of partitions of n such that m(greatest part) < m(1), where m = multiplicity.

0, 0, 0, 0, 1, 2, 3, 6, 8, 13, 18, 27, 35, 52, 67, 93, 121, 164, 209, 279, 353, 461, 582, 748, 935, 1191, 1480, 1861, 2302, 2870, 3526, 4365, 5335, 6554, 7976, 9736, 11789, 14316, 17259, 20844, 25032, 30092, 35992, 43086, 51347, 61215, 72710, 86361, 102235

Offset: 0

Author

Clark Kimberling, Apr 01 2014

Keywords

• nonn
• easy

Examples

			a(7) counts these 6 partitions:  511, 4111, 3211, 31111, 22111, 211111.
		

Crossrefs

Cf. A240077, A240078, A117995, A240080.

Programs

Mathematica

z = 60; f[n_] := f[n] = IntegerPartitions[n]; t1 = Table[Count[f[n], p_ /; Count[p, Max[p]] < Count[p, 1]], {n, 0, z}]  (* A240076 *)
t2 = Table[Count[f[n], p_ /; Count[p, Max[p]] <= Count[p, 1]], {n, 0, z}] (* A240077 *)
t3 = Table[Count[f[n], p_ /; Count[p, Max[p]] == Count[p, 1]], {n, 0, z}] (* A240078 *)
t4 = Table[Count[f[n], p_ /; Count[p, Max[p]] > Count[p, 1]], {n, 0, z}] (* A117995 *)
t5 = Table[Count[f[n], p_ /; Count[p, Max[p]] >= Count[p, 1]], {n, 0, z}] (* A240080 *)

Formula

a(n) + A240078(n) + A240080(n) = A000041 for n >= 0.