This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A339164 #6 Nov 25 2020 21:21:31 %S A339164 0,0,0,1,0,0,0,2,2,2,2,2,8,8,14,14,20,20,50,50,80,104,134,158,212,356, %T A339164 410,578,752,1040,1238,1646,1964,3236,3674,5066,6368,8720,10862,14078, %U A339164 17180,22076,31802,38378,49784,63824,82670,104150,136220,165980 %N A339164 Number of compositions (ordered partitions) of n into distinct parts, the least being 3. %H A339164 <a href="/index/Com#comp">Index entries for sequences related to compositions</a> %F A339164 G.f.: Sum_{k>=1} k! * x^(k*(k + 5)/2) / Product_{j=1..k-1} (1 - x^j). %e A339164 a(12) = 8 because we have [9, 3], [5, 4, 3], [5, 3, 4], [4, 5, 3], [4, 3, 5], [3, 9], [3, 5, 4] and [3, 4, 5]. %p A339164 b:= proc(n, i, p) option remember; %p A339164 `if`(n=0, p!, `if`((i-3)*(i+4)/2<n, 0, %p A339164 add(b(n-i*j, i-1, p+j), j=0..min(1, n/i)))) %p A339164 end: %p A339164 a:= n-> `if`(n<3, 0, b(n-3$2, 1)): %p A339164 seq(a(n), n=0..55); # _Alois P. Heinz_, Nov 25 2020 %t A339164 nmax = 49; CoefficientList[Series[Sum[k! x^(k (k + 5)/2)/Product[1 - x^j, {j, 1, k - 1}], {k, 1, nmax}], {x, 0, nmax}], x] %Y A339164 Cf. A026796, A026824, A339101, A339162, A339163, A339165, A339166. %K A339164 nonn %O A339164 0,8 %A A339164 _Ilya Gutkovskiy_, Nov 25 2020