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 A237751 Number of partitions of n such that 2*(greatest part) < (number of parts). 5
 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 (list; graph; refs; listen; history; text; internal format)
 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.  A237751(n) + A237755(n) = A000041(n). LINKS 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 Cf. A064173, A237752-A237757, A000041. Sequence in context: A260183 A134157 A274194 * A045476 A323360 A297417 Adjacent sequences:  A237748 A237749 A237750 * A237752 A237753 A237754 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 13 2014 STATUS approved

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Last modified September 22 03:21 EDT 2020. Contains 337289 sequences. (Running on oeis4.)