A240078 Number of partitions of n such that m(greatest part) = m(1), where m = multiplicity.

1, 1, 1, 2, 2, 2, 4, 3, 6, 6, 10, 9, 18, 16, 27, 29, 44, 46, 71, 75, 109, 122, 167, 188, 257, 290, 382, 442, 569, 657, 840, 971, 1220, 1423, 1761, 2054, 2528, 2944, 3586, 4189, 5061, 5901, 7095, 8262, 9869, 11496, 13652, 15875, 18786, 21805, 25685, 29790

Offset: 0

Author

Clark Kimberling, Apr 01 2014

Keywords

• nonn
• easy

Examples

			a(7) counts these 3 partitions:  61, 421, 1111111.
		

Crossrefs

Cf. A240076, A240077, 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

A240076(n) + a(n) + A240079(n) = A000041(n) for n >= 0.