A339171 - OEIS

%I #5 Nov 26 2020 09:16:52

%S 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,2,2,2,2,2,2,2,2,2,2,8,8,14,14,20,

%T 20,26,26,32,32,38,62,68,92,122,146,176,224,254,302,356,404,458,650,

%U 704,896,1094,1406,1604,2060,2378,2954,3416,4112,4694,5654,7076,8156,9842

%N Number of compositions (ordered partitions) of n into distinct parts, the least being 8.

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

%F G.f.: Sum_{k>=1} k! * x^(k*(k + 15)/2) / Product_{j=1..k-1} (1 - x^j).

%e a(27) = 8 because we have [19, 8], [10, 9, 8], [10, 8, 9], [9, 10, 8], [9, 8, 10], [8, 19], [8, 10, 9] and [8, 9, 10].

%t nmax = 65; CoefficientList[Series[Sum[k! x^(k (k + 15)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A026801, A026829, A339109, A339162, A339163, A339164, A339165, A339166, A339169, A339170, A339172.

%K nonn

%O 0,18

%A _Ilya Gutkovskiy_, Nov 25 2020