%I #4 Sep 08 2021 08:01:13

%S 1,1,1,2,2,3,4,5,6,8,10,12,15,18,22,27,32,38,46,54,64,76,89,104,122,

%T 142,165,192,221,255,294,337,385,441,501,570,646,731,824,930,1043,

%U 1171,1310,1464,1630,1817,2015,2236,2473,2734,3013,3322,3648,4008,4391,4809,5252,5738,6249

%N Number of partitions of n into at most 6 distinct parts.

%H <a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1).

%F G.f.: Sum_{k=0..6} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).

%t nmax = 58; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 6}], {x, 0, nmax}], x]

%t Join[{1}, LinearRecurrence[{1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76}, 58]]

%Y Cf. A001402, A014591, A065033, A347586, A347587.

%K nonn,easy

%O 0,4

%A _Ilya Gutkovskiy_, Sep 08 2021