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%I #5 Mar 12 2014 12:56:28
%S 1,1,1,1,2,1,2,2,3,2,4,2,6,4,6,4,10,5,12,7,16,8,20,10,27,14,32,16,44,
%T 19,53,25,69,31,84,36,108,47,130,55,167,67,202,83,252,99,305,119,380,
%U 146,456,173,564,208,676,250,826,298,991,352,1205,424,1435
%N Number of palindromic partitions of n whose least part has multiplicity 1.
%C Palindromic partitions are defined at A025065.
%e a(11) counts these partitions (written as palindromes): [11], [5,1,5], [4,3,4], [2,3,1,3,2].
%t z = 40; p[n_, k_] := Select[IntegerPartitions[n], (Count[OddQ[Transpose[Tally[#]][[2]]], True] <= 1) && (Count[#, Min[#]] == k) &]
%t Table[p[n, 1], {n, 1, 12}]
%t t1 = Table[Length[p[n, 1]], {n, 1, z}] (* A238781 *)
%t Table[p[n, 2], {n, 1, 12}]
%t t2 = Table[Length[p[n, 2]], {n, 1, z}] (* A238782 *)
%t Table[p[n, 3], {n, 1, 12}]
%t t3 = Table[Length[p[n, 3]], {n, 1, z}] (* A238783 *)
%t Table[p[n, 4], {n, 1, 12}]
%t t4 = Table[Length[p[n, 4]], {n, 1, z}] (* A238784 *)
%t (* _Peter J. C. Moses_, Mar 03 2014 *)
%Y Cf. A025065, A238782, A238783, A238784, A238779.
%K nonn,easy
%O 1,5
%A _Clark Kimberling_, Mar 05 2014