A240076 - OEIS

%I #6 Apr 06 2014 04:18:01

%S 0,0,0,0,1,2,3,6,8,13,18,27,35,52,67,93,121,164,209,279,353,461,582,

%T 748,935,1191,1480,1861,2302,2870,3526,4365,5335,6554,7976,9736,11789,

%U 14316,17259,20844,25032,30092,35992,43086,51347,61215,72710,86361,102235

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

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

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

%t 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 t2 = Table[Count[f[n], p_ /; Count[p, Max[p]] <= Count[p, 1]], {n, 0, z}] (* A240077 *)

%t t3 = Table[Count[f[n], p_ /; Count[p, Max[p]] == Count[p, 1]], {n, 0, z}] (* A240078 *)

%t t4 = Table[Count[f[n], p_ /; Count[p, Max[p]] > Count[p, 1]], {n, 0, z}] (* A117995 *)

%t t5 = Table[Count[f[n], p_ /; Count[p, Max[p]] >= Count[p, 1]], {n, 0, z}] (* A240080 *)

%Y Cf. A240077, A240078, A117995, A240080.

%K nonn,easy

%O 0,6

%A _Clark Kimberling_, Apr 01 2014