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

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (24,-144).

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

Mathematica

a[n_]:=n*12^(n-1); a[Range[0, 40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)

Prog

(Magma) [n*12^(n-1): n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
(SageMath) [12^(n-1)*n for n in range(31)] # G. C. Greubel, Jan 16 2024

Crossrefs

Cf. A038327, A053541, A081127.

Sequence in context: A051546 A209448 A264504 * A059158 A062149 A231318

Adjacent sequences: A081125 A081126 A081127 * A081129 A081130 A081131

Keyword

easy,nonn

Author

Paul Barry, Mar 07 2003

Status

approved