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A237751
Number of partitions of n such that 2*(greatest part) < (number of parts).
9
0, 0, 1, 1, 1, 2, 3, 4, 6, 8, 10, 14, 18, 24, 32, 41, 52, 67, 85, 107, 135, 169, 210, 263, 324, 400, 493, 604, 736, 899, 1091, 1322, 1599, 1929, 2319, 2787, 3336, 3989, 4760, 5669, 6734, 7994, 9465, 11192, 13211, 15571, 18319, 21531, 25257, 29594, 34626
OFFSET
1,6
COMMENTS
Also, the number of partitions of n such that (greatest part) > 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) < 0.
LINKS
FORMULA
a(n) = A000041(n) - A237755(n).
EXAMPLE
a(6) = 2 counts these partitions: 21111, 111111.
MATHEMATICA
z = 55; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] < Length[p]], {n, z}]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 13 2014
STATUS
approved