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 A115327 #39 Apr 17 2023 16:30:23
%S A115327 1,1,4,10,46,166,856,3844,21820,114076,703216,4125496,27331624,
%T A115327 175849480,1241782816,8627460976,64507687696,478625814544,
%U A115327 3768517887040,29614311872416,244419831433696,2021278543778656,17419727924101504
%N A115327 E.g.f.: exp(x + 3/2*x^2).
%C A115327 Term-by-term square of sequence with e.g.f.: exp(x+m/2*x^2) is given by e.g.f.: exp(x/(1-m*x))/sqrt(1-m^2*x^2) for all m.
%C A115327 a(n) is also the number of square roots of any permutation in S_{3n} whose disjoint cycle decomposition consists of n cycles of length 3. - _Luis Manuel Rivera Martínez_, Feb 26 2015
%H A115327 Vincenzo Librandi, <a href="/A115327/b115327.txt">Table of n, a(n) for n = 0..200</a>
%H A115327 John Campbell, <a href="https://dmtcs.episciences.org/3210">A class of symmetric difference-closed sets related to commuting involutions</a>, Discrete Mathematics & Theoretical Computer Science, Vol 19 no. 1, 2017.
%H A115327 Jesús Leaños, Rutilo Moreno, and Luis Manuel Rivera-Martínez, <a href="http://arxiv.org/abs/1005.1531">On the number of mth roots of permutations</a>, arXiv:1005.1531 [math.CO], 2010-2011.
%H A115327 Jesús Leaños, Rutilo Moreno, and Luis Manuel Rivera-Martínez, <a href="http://ajc.maths.uq.edu.au/pdf/52/ajc_v52_p041.pdf">On the number of mth roots of permutations</a>, Australas. J. Combin. 52 (2012), 41-54, (Theorems 1 and 2).
%F A115327 Term-by-term square equals A115328 which has e.g.f.: exp(x/(1-3*x))/sqrt(1-9*x^2).
%F A115327 From _Paul Barry_, Apr 10 2009: (Start)
%F A115327 G.f.: 1/(1-x-3*x^2/(1-x-6*x^2/(1-x-9*x^2/(1-x-12*x^2/(1-... (continued fraction);
%F A115327 a(n) = a(n-1)+3*(n-1)*a(n-2). (End)
%F A115327 a(n) ~ exp(sqrt(n/3)-n/2-1/12)*3^(n/2)*n^(n/2)/sqrt(2). - _Vaclav Kotesovec_, Oct 19 2012
%F A115327 G.f.: 1/Q(0), where Q(k)= 1 + 3*x*k - x/(1 - 3*x*(k+1)/Q(k+1)); (continued fraction). - _Sergei N. Gladkovskii_, Apr 17 2013
%F A115327 a(n) = n!*Sum_{k=0..floor(n/2)}3^k/(2^k*k!*(n-2*k)!). - _Luis Manuel Rivera Martínez_, Feb 26 2015
%t A115327 Range[0, 20]! CoefficientList[Series[Exp[(x + 3 / 2 x^2)], {x, 0, 20}], x] (* _Vincenzo Librandi_, May 22 2013 *)
%o A115327 (PARI) a(n)=local(m=3);n!*polcoeff(exp(x+m/2*x^2+x*O(x^n)),n)
%Y A115327 Column k=3 of A359762.
%Y A115327 Cf. A115328.
%K A115327 nonn
%O A115327 0,3
%A A115327 _Paul D. Hanna_, Jan 20 2006