A347587 Number of partitions of n into at most 5 distinct parts.

1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 75, 88, 102, 119, 137, 158, 181, 207, 235, 268, 302, 341, 383, 430, 480, 536, 595, 661, 731, 808, 889, 979, 1073, 1176, 1285, 1403, 1527, 1662, 1803, 1956, 2116, 2288, 2468, 2662, 2864, 3080, 3306, 3547

Offset: 0

Author

Ilya Gutkovskiy, Sep 08 2021

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,-1,-1,1,1,1,0,0,-1,-1,1).

Crossrefs

Cf. A001401, A014591, A065033, A347586, A347588.

Programs

Mathematica

nmax = 58; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 5}], {x, 0, nmax}], x]
LinearRecurrence[{1, 1, 0, 0, -1, -1, -1, 1, 1, 1, 0, 0, -1, -1, 1}, {1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22}, 59]

Formula

G.f.: Sum_{k=0..5} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).