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A081128 12th binomial transform of (0,1,0,0,0,0,0,0,...).

%I A081128 #27 Jan 16 2024 06:56:13
%S A081128 0,1,24,432,6912,103680,1492992,20901888,286654464,3869835264,
%T A081128 51597803520,681091006464,8916100448256,115909305827328,
%U A081128 1497904875307008,19258776968232960,246512345193381888
%N A081128 12th binomial transform of (0,1,0,0,0,0,0,0,...).
%H A081128 Vincenzo Librandi, <a href="/A081128/b081128.txt">Table of n, a(n) for n = 0..200</a>
%H A081128 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (24,-144).
%F A081128 a(n) = 24*a(n-1) - 132*a(n-2), a(0)=0, a(1)=1.
%F A081128 a(n) = n*12^(n-1).
%F A081128 G.f.: x/(1-12*x)^2.
%F A081128 From _Amiram Eldar_, Oct 28 2020: (Start)
%F A081128 Sum_{n>=1} 1/a(n) = 12*log(12/11).
%F A081128 Sum_{n>=1} (-1)^(n+1)/a(n) = 12*log(13/12). (End)
%F A081128 E.g.f.: x*exp(12*x). - _G. C. Greubel_, Jan 16 2024
%t A081128 a[n_]:=n*12^(n-1); a[Range[0,40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011 *)
%o A081128 (Magma) [n*12^(n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 06 2011
%o A081128 (SageMath) [12^(n-1)*n for n in range(31)] # _G. C. Greubel_, Jan 16 2024
%Y A081128 Cf. A038327, A053541, A081127.
%K A081128 easy,nonn
%O A081128 0,3
%A A081128 _Paul Barry_, Mar 07 2003