A238589 - OEIS

A238589

Number of partitions p of n such that 2*min(p) is a part of p.

0, 0, 1, 1, 2, 4, 5, 8, 13, 17, 24, 36, 47, 64, 88, 116, 153, 203, 261, 340, 439, 559, 710, 905, 1136, 1427, 1786, 2223, 2756, 3415, 4201, 5167, 6330, 7730, 9413, 11449, 13864, 16767, 20225, 24344, 29228, 35045, 41898, 50029, 59609, 70899, 84165, 99785, 118052

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = A000041(n) - A238594(n).

G.f.: Sum_{k>=1} x^(3*k)/Product_{j>=k} (1-x^j). - Seiichi Manyama, May 17 2023

EXAMPLE

a(6) counts these partitions: 42, 321, 2211, 21111.

MATHEMATICA

Table[Count[IntegerPartitions[n], p_ /; MemberQ[p, 2*Min[p]]], {n, 50}]