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%I #6 Nov 25 2020 21:13:11
%S 0,0,0,0,1,0,0,0,0,2,2,2,2,2,2,8,8,14,14,20,20,26,50,56,80,110,134,
%T 164,212,242,410,464,632,806,1118,1292,1724,2042,2594,3752,4448,5726,
%U 7382,9524,12020,15122,18602,23264,28424,39830,46670,60476,74780
%N Number of compositions (ordered partitions) of n into distinct parts, the least being 4.
%H <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F G.f.: Sum_{k>=1} k! * x^(k*(k + 7)/2) / Product_{j=1..k-1} (1 - x^j).
%e a(15) = 8 because we have [11, 4], [6, 5, 4], [6, 4, 5], [5, 6, 4], [5, 4, 6], [4, 11], [4, 6, 5] and [4, 5, 6].
%p b:= proc(n, i, p) option remember;
%p `if`(n=0, p!, `if`((i-4)*(i+5)/2<n, 0,
%p add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
%p end:
%p a:= n-> `if`(n<4, 0, b(n-4$2, 1)):
%p seq(a(n), n=0..55); # _Alois P. Heinz_, Nov 25 2020
%t nmax = 52; CoefficientList[Series[Sum[k! x^(k (k + 7)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A026797, A026825, A339102, A339162, A339163, A339164, A339166.
%K nonn
%O 0,10
%A _Ilya Gutkovskiy_, Nov 25 2020
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