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A347586
Number of partitions of n into at most 4 distinct parts.
8
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 26, 31, 36, 43, 49, 57, 65, 75, 84, 96, 107, 121, 134, 150, 165, 184, 201, 222, 242, 266, 288, 315, 340, 370, 398, 431, 462, 499, 533, 573, 611, 655, 696, 744, 789, 841, 890, 946, 999, 1060, 1117, 1182, 1244, 1314, 1380, 1455
OFFSET
0,4
FORMULA
G.f.: Sum_{k=0..4} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).
a(n) ~ A000578(n)/144. - Stefano Spezia, Sep 08 2021
MATHEMATICA
nmax = 60; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 4}], {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 1, 0, 0, -2, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10}, 60]]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Sep 08 2021
STATUS
approved