A240312 - OEIS

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A240312

Number of partitions p of n such that (maximal multiplicity of the parts of p) = (maximal part of p).

1, 1, 0, 0, 2, 1, 2, 0, 2, 3, 5, 5, 9, 7, 11, 11, 18, 15, 28, 27, 41, 43, 62, 64, 91, 96, 127, 140, 184, 200, 260, 287, 365, 410, 511, 573, 717, 803, 985, 1120, 1359, 1538, 1859, 2106, 2522, 2870, 3407, 3872, 4586, 5207, 6128, 6976, 8167, 9284, 10844, 12321

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..55.

FORMULA

a(n) = A240311(n) - A240310(n) for n >= 0.

a(n) + A240310(n) + A240314(n) = A000041(n) for n >= 0.

EXAMPLE

a(6) counts these 2 partitions: 3111, 2211.

MATHEMATICA

z = 60; f[n_] := f[n] = IntegerPartitions[n]; m[p_] := Max[Map[Length, Split[p]]] (* maximal multiplicity *)