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EXAMPLE
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a(4) = 1 from the partition (5,1,1,1) of 4*2 = 8 with 4 parts, at least one part > 4.
a(5) = 18 from the following partitions of 15: (11,1,1,1,1), (10,2,1,1,1), (9,3,1,1,1), (9,2,2,1,1), (8,4,1,1,1), (8,3,2,1,1),(8,2,2,1,1), (7,5,1,1,1), (7,4,2,1,1), (7,3,3,1,1), (7,3,2,2,1), (7,2,2,2,2), (6,6,1,1,1), (6,5,2,1,1), (6,4,3,1,1), (6,4,2,2,1), (6,3,3,2,1), (6,3,2,2,2).
18 = 1 + 1 + 2 + 3 + 5 + 6.
For n=7 sum the following number of partitions: for 29 the number of 6-part partitions for 6, for 28 the 6-part partitions of 7, ..., up to the 6-part partitions of 27 for 8.
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