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%I #7 Mar 08 2014 22:51:50
%S 0,1,1,2,2,3,4,5,6,9,11,14,19,24,31,41,51,65,84,105,132,167,207,257,
%T 321,395,486,599,731,892,1089,1319,1597,1933,2327,2798,3361,4021,4805,
%U 5736,6825,8109,9625,11393,13469,15905,18738,22049,25915,30401,35620
%N Number of partitions p of n such that 1 + (1/2)*max(p) is a part of p.
%H Giovanni Resta, <a href="/A238625/b238625.txt">Table of n, a(n) for n = 1..1000</a>
%e a(6) counts these partitions: 222, 2211, 21111.
%t Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 1 + Max[p]/2]], {n, 50}]
%t p[n_, m_] := If[m > n, 0, If[n == m, 1, p[n, m] = Sum[p[n - m, j], {j, m}]]]; a[1] = 0; a[n_] := 1 + Sum[p[n-k-1, 2*k], {k, n/2}]; Array[a,100] (* _Giovanni Resta_, Mar 07 2014 *)
%Y Cf. A238479, A238624.
%K nonn,easy
%O 1,4
%A _Clark Kimberling_, Mar 02 2014