A339089 - OEIS

%I #4 Nov 23 2020 17:09:02

%S 1,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,2,1,0,0,0,0,2,1,0,0,0,0,4,1,0,0,0,6,

%T 4,1,0,0,0,6,6,1,0,0,0,12,6,1,0,0,0,18,8,1,0,0,24,24,8,1,0,0,24,30,10,

%U 1,0,0,48,42,10,1,0,0,72,48,12,1,0,0,120,60,12,1,0,120,144

%N Number of compositions (ordered partitions) of n into distinct parts congruent to 5 mod 6.

%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>

%F G.f.: Sum_{k>=0} k! * x^(k*(3*k + 2)) / Product_{j=1..k} (1 - x^(6*j)).

%e a(33) = 6 because we have [17, 11, 5], [17, 5, 11], [11, 17, 5], [11, 5, 17], [5, 17, 11] and [5, 11, 17].

%t nmax = 86; CoefficientList[Series[Sum[k! x^(k (3 k + 2))/Product[1 - x^(6 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

%Y Cf. A016969, A017837, A032020, A032021, A109702, A281244, A337547, A337548, A339059, A339060, A339086, A339087, A339088.

%K nonn

%O 0,17

%A _Ilya Gutkovskiy_, Nov 23 2020