A347587 - OEIS

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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

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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