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%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
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