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 A332031 #17 Dec 15 2021 17:46:52
%S A332031 1,1,1,3,1,3,1,3,7,3,1,9,1,3,7,27,1,9,1,27,7,3,1,33,121,3,7,27,1,129,
%T A332031 1,27,7,3,121,753,1,3,7,147,1,729,1,27,127,3,1,753,5041,123,7,27,1,
%U A332031 729,121,5067,7,3,1,873,1,3,5047,40347,121,729,1,27,7,5163,1,41073,1,3,127
%N A332031 G.f.: Sum_{k>=1} k! * x^(k^2) / (1 - x^k).
%C A332031 Number of compositions (ordered partitions) of n into distinct parts where either all parts are odd or all parts are even, and where every odd part or even part between the largest and smallest appears.
%C A332031 Number of compositions of n that are either singular compositions (just [n]), or where the difference between successive parts is always 2. - _Antti Karttunen_, Dec 15 2021
%H A332031 Antti Karttunen, <a href="/A332031/b332031.txt">Table of n, a(n) for n = 1..10000</a>
%F A332031 From _Antti Karttunen_, Dec 15 2021: (Start)
%F A332031 a(n) = Sum_{d|n, d <= n/d} d!.
%F A332031 a(2n-1) = A332032(2n-1) for all n >= 1.
%F A332031 (End)
%e A332031 a(12) = 9 because we have [12], [7, 5], [6, 4, 2], [6, 2, 4], [5, 7], [4, 6, 2], [4, 2, 6], [2, 6, 4] and [2, 4, 6].
%t A332031 nmax = 75; CoefficientList[Series[Sum[k! x^(k^2)/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%o A332031 (PARI) A332031(n) = sumdiv(n, d, (d<=(n/d)) * d!); \\ _Antti Karttunen_, Dec 15 2021
%Y A332031 Cf. A000142, A008578 (positions of 1's), A038548, A066839, A107461.
%Y A332031 Coincides with A332032 on odd numbers.
%K A332031 nonn,look
%O A332031 1,4
%A A332031 _Ilya Gutkovskiy_, Feb 05 2020