A240080 Number of partitions of n such that m(greatest part) >= m(1), where m = multiplicity.

1, 1, 2, 3, 4, 5, 8, 9, 14, 17, 24, 29, 42, 49, 68, 83, 110, 133, 176, 211, 274, 331, 420, 507, 640, 767, 956, 1149, 1416, 1695, 2078, 2477, 3014, 3589, 4334, 5147, 6188, 7321, 8756, 10341, 12306, 14491, 17182, 20175, 23828, 27919, 32848, 38393, 45038, 52505

Offset: 0

Author

Clark Kimberling, Apr 01 2014

Keywords

• nonn
• easy

Examples

			a(7) counts these 9 partitions:  7, 61, 52, 43, 421, 331, 322, 2221, 1111111.
		

Crossrefs

Cf. A240076, A240077, A240078, A117995.

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) + A117995(n) for n >= 0.