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 A097814 #14 Jan 27 2019 18:04:59
%S A097814 1,6,45,432,5265,79218,1426653,29961900,719092161,19415508030,
%T A097814 582465299949,19221355075464,691968783248145,26986782548271978,
%U A097814 1133444867032206045,51005019016463620932,2448240912790296851457
%N A097814 E.g.f. exp(3x)/(1-3x).
%H A097814 Michael Z. Spivey and Laura L. Steil, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL9/Spivey/spivey7.html">The k-Binomial Transforms and the Hankel Transform</a>, Journal of Integer Sequences, Vol. 9 (2006), Article 06.1.1.
%F A097814 a(n) = 3n*a(n-1)+3^n, n>0, a(0)=1; a(n) = 3^n*A000522(n).
%F A097814 G.f.: 1/Q(0), where Q(k) = 1 - 6*x*(k+1) - 9*x^2*(k+1)^2/Q(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Sep 30 2013
%F A097814 Conjecture: a(n) +3*(-n-1)*a(n-1) +9*(n-1)*a(n-2)=0. - _R. J. Mathar_, Dec 21 2014
%t A097814 With[{nn=20},CoefficientList[Series[Exp[3x]/(1-3x),{x,0,nn}],x] Range[ 0,nn]!] (* or *) RecurrenceTable[{a[0]==1,a[n]==3n a[n-1]+3^n},a,{n,20}] (* _Harvey P. Dale_, Feb 23 2012 *)
%Y A097814 Cf. A082032.
%K A097814 easy,nonn
%O A097814 0,2
%A A097814 _Paul Barry_, Aug 26 2004