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A339104 Number of compositions (ordered partitions) of n into distinct parts >= 6.

%I A339104 #5 Nov 23 2020 21:15:50
%S A339104 1,0,0,0,0,0,1,1,1,1,1,1,1,3,3,5,5,7,7,9,9,17,17,25,31,39,45,59,65,79,
%T A339104 115,129,165,209,269,313,403,471,585,683,941,1063,1375,1641,2097,2537,
%U A339104 3161,3745,4663,5535,6741,8627,10241,12535,15307,18849,22869,28409
%N A339104 Number of compositions (ordered partitions) of n into distinct parts >= 6.
%H A339104 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A339104 G.f.: Sum_{k>=0} k! * x^(k*(k + 11)/2) / Product_{j=1..k} (1 - x^j).
%e A339104 a(13) = 3 because we have [13], [7, 6] and [6, 7].
%p A339104 b:= proc(n, i, p) option remember;
%p A339104       `if`(n=0, p!, `if`((i-5)*(i+6)/2<n, 0,
%p A339104        add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
%p A339104     end:
%p A339104 a:= n-> b(n$2, 0):
%p A339104 seq(a(n), n=0..60);  # _Alois P. Heinz_, Nov 23 2020
%t A339104 nmax = 57; CoefficientList[Series[Sum[k! x^(k (k + 11)/2)/Product[1 - x^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]
%Y A339104 Cf. A017900, A025151, A032020, A032022, A185326, A339101, A339102, A339103.
%K A339104 nonn
%O A339104 0,14
%A A339104 _Ilya Gutkovskiy_, Nov 23 2020