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%I #5 Nov 23 2020 17:08:54
%S 1,1,0,0,0,0,0,1,2,0,0,0,0,1,2,0,0,0,0,1,4,6,0,0,0,1,4,6,0,0,0,1,6,12,
%T 0,0,0,1,6,18,24,0,0,1,8,24,24,0,0,1,8,30,48,0,0,1,10,42,72,0,0,1,10,
%U 48,120,120,0,1,12,60,144,120,0,1,12,72,216,240,0,1,14,84,264,360
%N Number of compositions (ordered partitions) of n into distinct parts congruent to 1 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(21) = 6 because we have [13, 7, 1], [13, 1, 7], [7, 13, 1], [7, 1, 13], [1, 13, 7] and [1, 7, 13].
%t nmax = 83; 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. A005708, A016921, A032020, A032021, A109701, A280456, A337547, A337548, A339059, A339060, A339086, A339087, A339089.
%K nonn
%O 0,9
%A _Ilya Gutkovskiy_, Nov 23 2020
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