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

0,4

Links

Table of n, a(n) for n=0..58.

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

Formula

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

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]

Crossrefs

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

Sequence in context: A288000 A034149 A034150 * A288001 A034321 A034320

Adjacent sequences: A347584 A347585 A347586 * A347588 A347589 A347590

Keyword

nonn,easy

Author

Ilya Gutkovskiy, Sep 08 2021

Status

approved