A347548 Number of partitions of n into 3 or more distinct parts.

1, 1, 2, 3, 5, 6, 9, 11, 15, 19, 24, 29, 37, 44, 54, 65, 78, 92, 110, 129, 152, 178, 208, 241, 281, 324, 374, 431, 495, 567, 650, 741, 845, 962, 1093, 1239, 1405, 1588, 1794, 2025, 2281, 2566, 2886, 3239, 3633, 4071, 4556, 5093, 5691, 6350, 7080, 7888, 8779, 9762, 10850

Offset: 6

Author

Ilya Gutkovskiy, Sep 06 2021

Keywords

• nonn

Crossrefs

Cf. A000009, A004526, A111133, A347549.

Programs

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 3, nmax}], {x, 0, nmax}], x] // Drop[#, 6] &

Formula

G.f.: Sum_{k>=3} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

a(n) = A000009(n) - floor((n + 1)/2). - Vaclav Kotesovec, Sep 14 2021