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

%I A240078 #5 Apr 06 2014 04:18:18
%S A240078 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,
%T A240078 290,382,442,569,657,840,971,1220,1423,1761,2054,2528,2944,3586,4189,
%U A240078 5061,5901,7095,8262,9869,11496,13652,15875,18786,21805,25685,29790
%N A240078 Number of partitions of n such that m(greatest part) = m(1), where m = multiplicity.
%F A240078 A240076(n) + a(n) + A240079(n) = A000041(n) for n >= 0.
%e A240078 a(7) counts these 3 partitions:  61, 421, 1111111.
%t A240078 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 *)
%t A240078 t2 = Table[Count[f[n], p_ /; Count[p, Max[p]] <= Count[p, 1]], {n, 0, z}] (* A240077 *)
%t A240078 t3 = Table[Count[f[n], p_ /; Count[p, Max[p]] == Count[p, 1]], {n, 0, z}] (* A240078 *)
%t A240078 t4 = Table[Count[f[n], p_ /; Count[p, Max[p]] > Count[p, 1]], {n, 0, z}] (* A117995 *)
%t A240078 t5 = Table[Count[f[n], p_ /; Count[p, Max[p]] >= Count[p, 1]], {n, 0, z}] (* A240080 *)
%Y A240078 Cf. A240076, A240077, A117995, A240080.
%K A240078 nonn,easy
%O A240078 0,4
%A A240078 _Clark Kimberling_, Apr 01 2014