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%I #5 Nov 23 2020 17:08:36
%S 1,1,0,0,0,0,1,2,0,0,0,1,2,0,0,0,1,4,6,0,0,1,4,6,0,0,1,6,12,0,0,1,6,
%T 18,24,0,1,8,24,24,0,1,8,30,48,0,1,10,42,72,0,1,10,48,120,120,1,12,60,
%U 144,120,1,12,72,216,240,1,14,84,264,360,1,14,96,360,600,1,16,114
%N Number of compositions (ordered partitions) of n into distinct parts congruent to 1 mod 5.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: Sum_{k>=0} k! * x^(k*(5*k - 3)/2) / Product_{j=1..k} (1 - x^(5*j)).
%e a(18) = 6 because we have [11, 6, 1], [11, 1, 6], [6, 11, 1], [6, 1, 11], [1, 11, 6] and [1, 6, 11].
%t nmax = 78; CoefficientList[Series[Sum[k! x^(k (5 k - 3)/2)/Product[1 - x^(5 j), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A003520, A016861, A032020, A032021, A109697, A280454, A337547, A337548, A339059, A339060, A339087, A339088, A339089.
%K nonn
%O 0,8
%A _Ilya Gutkovskiy_, Nov 23 2020