A347549 Number of partitions of n into 4 or more distinct parts.

1, 1, 2, 3, 5, 7, 10, 13, 18, 23, 30, 38, 48, 59, 73, 89, 108, 130, 156, 185, 220, 259, 304, 356, 415, 482, 559, 645, 743, 854, 979, 1119, 1278, 1455, 1654, 1878, 2127, 2405, 2717, 3063, 3449, 3879, 4356, 4885, 5474, 6125, 6846, 7645, 8527, 9501, 10579

Offset

10,3

Links

Table of n, a(n) for n=10..60.

Formula

G.f.: Sum_{k>=4} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

a(n) = A000009(n) - A014591(n). - Vaclav Kotesovec, Sep 14 2021

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 4, nmax}], {x, 0, nmax}], x] // Drop[#, 10] &

Crossrefs

Cf. A000009, A014591, A111133, A347548.

Sequence in context: A001401 A373078 A377076 * A008628 A363067 A038499

Adjacent sequences: A347546 A347547 A347548 * A347550 A347551 A347552

Keyword

nonn

Author

Ilya Gutkovskiy, Sep 06 2021

Status

approved