cp's OEIS Frontend

A339166 Number of compositions (ordered partitions) of n into distinct parts, the least being 5.

%I A339166 #5 Nov 25 2020 20:20:25
%S A339166 0,0,0,0,0,1,0,0,0,0,0,2,2,2,2,2,2,2,8,8,14,14,20,20,26,26,56,56,86,
%T A339166 110,140,164,218,242,296,464,518,686,884,1172,1370,1802,2120,2672,
%U A339166 3134,4526,5108,6764,8186,10682,13088,16544,19790,24950,29876,36716
%N A339166 Number of compositions (ordered partitions) of n into distinct parts, the least being 5.
%H A339166 <a href="/index/Com#comp">Index entries for sequences related to compositions</a>
%F A339166 G.f.: Sum_{k>=1} k! * x^(k*(k + 9)/2) / Product_{j=1..k-1} (1 - x^j).
%e A339166 a(18) = 8 because we have [13, 5], [7, 6, 5], [7, 5, 6], [6, 7, 5], [6, 5, 7], [5, 13], [5, 7, 6] and [5, 6, 7].
%p A339166 b:= proc(n, i, p) option remember;
%p A339166       `if`(n=0, p!, `if`((i-5)*(i+6)/2<n, 0,
%p A339166        add(b(n-i*j, i-1, p+j), j=0..min(1, n/i))))
%p A339166     end:
%p A339166 a:= n-> `if`(n<5, 0, b(n-5$2, 1)):
%p A339166 seq(a(n), n=0..60);  # _Alois P. Heinz_, Nov 25 2020
%t A339166 nmax = 55; CoefficientList[Series[Sum[k! x^(k (k + 9)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x]
%Y A339166 Cf. A026798, A026826, A339103, A339162, A339163, A339164, A339165.
%K A339166 nonn
%O A339166 0,12
%A A339166 _Ilya Gutkovskiy_, Nov 25 2020