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 A069996 #24 Jan 03 2025 17:40:05
%S A069996 0,1,12,81,432,2025,8748,35721,139968,531441,1968300,7144929,25509168,
%T A069996 89813529,312487308,1076168025,3673320192,12440502369,41841412812,
%U A069996 139858796529,464904586800,1537671920841,5062810950252,16600580533161,54226471004352,176518460300625
%N A069996 Number of spanning trees on the bipartite graph K_{3,n}.
%C A069996 This is the second binomial transform of the octagonal numbers A000567 and the binomial transform of A084857. - _Paul Barry_, Jun 09 2003
%H A069996 Alois P. Heinz, <a href="/A069996/b069996.txt">Table of n, a(n) for n = 0..1000</a>
%H A069996 Wrath of Math, <a href="https://www.youtube.com/watch?v=_8JRLfjQrSs">2025 is a Strange Number</a>, YouTube video, 2025.
%H A069996 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-27,27).
%F A069996 a(n) = n^2 * 3^(n-1).
%F A069996 E.g.f.: exp(3*x)*(x+3*x^2). - _Paul Barry_, Jul 23 2003
%F A069996 From _Colin Barker_, Aug 10 2012: (Start)
%F A069996 a(n) = 9*a(n-1)-27*a(n-2)+27*a(n-3).
%F A069996 G.f.: x*(1+3*x)/(1-3*x)^3. (End)
%F A069996 G.f.: 1 + 12*x/(G(0) - 12*x), where G(k) = 1 + 12*x + 2*k*(6*x+1) + (1+3*x)*k^2 - 3*x*(k+1)^2*(k+3)^2/G(k+1); (continued fraction). - _Sergei N. Gladkovskii_, Jul 05 2013
%t A069996 a[n_] := n^2*3^(n - 1); Table[ a[n], {n, 1, 24}]
%Y A069996 Cf. A000567, A084857.
%K A069996 nonn,easy
%O A069996 0,3
%A A069996 Eric Weinhandl (eweinhandl(AT)msn.com), May 01 2002
%E A069996 Edited and extended by _Robert G. Wilson v_, May 04 2002
%E A069996 a(0)=0 prepended by _Alois P. Heinz_, Jan 03 2025