A081128 12th binomial transform of (0,1,0,0,0,0,0,0,...).
0, 1, 24, 432, 6912, 103680, 1492992, 20901888, 286654464, 3869835264, 51597803520, 681091006464, 8916100448256, 115909305827328, 1497904875307008, 19258776968232960, 246512345193381888
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (24,-144).
Programs
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Magma
[n*12^(n-1): n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
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Mathematica
a[n_]:=n*12^(n-1); a[Range[0,40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
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SageMath
[12^(n-1)*n for n in range(31)] # G. C. Greubel, Jan 16 2024
Formula
a(n) = 24*a(n-1) - 132*a(n-2), a(0)=0, a(1)=1.
a(n) = n*12^(n-1).
G.f.: x/(1-12*x)^2.
From Amiram Eldar, Oct 28 2020: (Start)
Sum_{n>=1} 1/a(n) = 12*log(12/11).
Sum_{n>=1} (-1)^(n+1)/a(n) = 12*log(13/12). (End)
E.g.f.: x*exp(12*x). - G. C. Greubel, Jan 16 2024