A240486 - OEIS

A240486

Number of partitions of n containing m(1) as a part, where m denotes multiplicity.

0, 1, 0, 1, 2, 2, 4, 5, 8, 10, 16, 19, 29, 36, 51, 63, 89, 108, 148, 182, 242, 297, 390, 475, 615, 750, 955, 1161, 1466, 1774, 2217, 2679, 3316, 3994, 4911, 5892, 7197, 8613, 10451, 12470, 15055, 17905, 21508, 25513, 30503, 36081, 42966, 50678, 60117, 70732

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OFFSET

0,5

LINKS

Table of n, a(n) for n=0..49.

EXAMPLE

a(6) counts these 5 partitions: 51, 421, 331, 3211, 2221.

MATHEMATICA

z = 60; f[n_] := f[n] = IntegerPartitions[n];

Table[Count[f[n], p_ /; MemberQ[p, Count[p, 1]]], {n, 0, z}] (* A240486 *)

Table[Count[f[n], p_ /; MemberQ[p, Count[p, 2]]], {n, 0, z}] (* A240487 *)

Table[Count[f[n], p_ /; MemberQ[p, Count[p, 3]]], {n, 0, z}] (* A240488 *)