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 A332032 #16 Dec 15 2021 17:39:11
%S A332032 1,0,1,2,1,0,1,2,7,0,1,2,1,0,7,26,1,0,1,2,7,0,1,26,121,0,7,2,1,0,1,26,
%T A332032 7,0,121,722,1,0,7,26,1,0,1,2,127,0,1,746,5041,0,7,2,1,0,121,26,7,0,1,
%U A332032 722,1,0,5047,40346,121,0,1,2,7,0,1,746,1,0,127
%N A332032 G.f.: Sum_{k>=1} k! * x^(k^2) / (1 - x^(2*k)).
%C A332032 Number of compositions (ordered partitions) of n into distinct odd parts, where every odd part between the largest and smallest appears.
%H A332032 Antti Karttunen, <a href="/A332032/b332032.txt">Table of n, a(n) for n = 1..10000</a>
%F A332032 From _Antti Karttunen_, Dec 15 2021: (Start)
%F A332032 a(n) = Sum_{d|n, d <= n/d, and both d and n/d are of the same parity as n} d!.
%F A332032 a(2n-1) = A332031(2n-1) for all n >= 1.
%F A332032 (End)
%e A332032 a(9) = 7 because we have [9], [5, 3, 1], [5, 1, 3], [3, 5, 1], [3, 1, 5], [1, 5, 3] and [1, 3, 5].
%e A332032 a(12) = 2 because we have [7, 5], and [5, 7]. - _Antti Karttunen_, Dec 15 2021
%t A332032 nmax = 75; CoefficientList[Series[Sum[k! x^(k^2)/(1 - x^(2 k)), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A332032 (PARI) A332032(n) = sumdiv(n, d, if(!((n+d)%2) && !((n+(n/d))%2) && (d<=(n/d)), d!, 0)); \\ _Antti Karttunen_, Dec 15 2021
%Y A332032 Cf. A016825 (positions of 0's), A032021, A034178, A038548, A107461, A220400.
%Y A332032 Coincides with A332031 on odd numbers.
%K A332032 nonn
%O A332032 1,4
%A A332032 _Ilya Gutkovskiy_, Feb 05 2020