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 A081142 #36 Sep 08 2022 08:45:09
%S A081142 0,0,1,36,864,17280,311040,5225472,83607552,1289945088,19349176320,
%T A081142 283787919360,4086546038784,57954652913664,811365140791296,
%U A081142 11234286564802560,154070215745863680,2095354934143746048
%N A081142 12th binomial transform of (0,0,1,0,0,0,...).
%C A081142 Starting at 1, the three-fold convolution of A001021 (powers of 12).
%H A081142 Vincenzo Librandi, <a href="/A081142/b081142.txt">Table of n, a(n) for n = 0..400</a>
%H A081142 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (36,-432,1728).
%F A081142 a(n) = 36*a(n-1) - 432*a(n-2) + 1728*a(n-3), a(0) = a(1) = 0, a(2) = 1.
%F A081142 a(n) = 12^(n-2)*binomial(n, 2).
%F A081142 G.f.: x^2/(1 - 12*x)^3.
%F A081142 a(n) = 2^(2*n-5)*3^(n-2)*n*(n-1). - _Harvey P. Dale_, Jul 25 2013
%F A081142 E.g.f.: (1/2)*exp(12*x)*x^2. - _Franck Maminirina Ramaharo_, Nov 23 2018
%F A081142 From _Amiram Eldar_, Jan 06 2022: (Start)
%F A081142 Sum_{n>=2} 1/a(n) = 24 - 264*log(12/11).
%F A081142 Sum_{n>=2} (-1)^n/a(n) = 312*log(13/12) - 24. (End)
%p A081142 seq(coeff(series(x^2/(1-12*x)^3,x,n+1), x, n), n = 0 .. 20); # _Muniru A Asiru_, Nov 24 2018
%t A081142 LinearRecurrence[{36,-432,1728},{0,0,1},30] (* or *) Table[(n-1) (n-2) 3^(n-3) 2^(2n-7),{n,20}] (* _Harvey P. Dale_, Jul 25 2013 *)
%o A081142 (Magma) [12^(n-2)* Binomial(n, 2): n in [0..20]]; // _Vincenzo Librandi_, Oct 16 2011
%o A081142 (PARI) vector(20, n, n--; 2^(2*n-5)*3^(n-2)*n*(n-1)) \\ _G. C. Greubel_, Nov 23 2018
%o A081142 (Sage) [2^(2*n-5)*3^(n-2)*n*(n-1) for n in range(20)] # _G. C. Greubel_, Nov 23 2018
%o A081142 (GAP) List([0..20],n->12^(n-2)*Binomial(n,2)); # _Muniru A Asiru_, Nov 24 2018
%Y A081142 Cf. A001021.
%Y A081142 Sequences similar to the form q^(n-2)*binomial(n, 2): A000217 (q=1), A001788 (q=2), A027472 (q=3), A038845 (q=4), A081135 (q=5), A081136 (q=6), A027474 (q=7), A081138 (q=8), A081139 (q=9), A081140 (q=10), A081141 (q=11), this sequence (q=12), A027476 (q=15).
%K A081142 easy,nonn
%O A081142 0,4
%A A081142 _Paul Barry_, Mar 08 2003