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%I #9 Mar 01 2014 15:54:10
%S 1,2,3,4,5,7,9,11,16,18,26,33,44,51,74,86,117,144,188,224,298,354,459,
%T 560,705,843,1069,1279,1596,1924,2365,2826,3471,4134,5036,6009,7252,
%U 8609,10369,12272,14687,17372,20674,24356,28920,33973,40160,47122,55471
%N Number of partitions p of n containing round((min(p) + max(p))/2) as a part.
%C As used here, if k is a positive integer, then round(k + 1/2) = k + 1.
%F a(n) + A238487(n) = A000041(n).
%e a(6) counts these partitions: 6, 33, 321, 222, 2211, 21111, 111111.
%t Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, Round[(Min[p] + Max[p])/2]]], {n, 30}]
%Y Cf. A238487.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_, Feb 27 2014