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a(n) = n*6^(n-1).
12

%I #56 Jan 22 2023 15:35:52

%S 1,12,108,864,6480,46656,326592,2239488,15116544,100776960,665127936,

%T 4353564672,28298170368,182849716224,1175462461440,7522959753216,

%U 47958868426752,304679870005248,1929639176699904,12187194800209920,76779327241322496,482612914088312832

%N a(n) = n*6^(n-1).

%C Binomial transform of A053464. - _R. J. Mathar_, Oct 26 2011

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H Vincenzo Librandi, <a href="/A053469/b053469.txt">Table of n, a(n) for n = 1..400</a>

%H Frank Ellermann, <a href="/A001792/a001792.txt">Illustration of binomial transforms</a>.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36).

%F a(n) = 12*a(n-1) - 36*a(n-2), n>=3.

%F G.f.: x/(6x-1)^2. - _Zerinvary Lajos_, Apr 28 2009

%F E.g.f.: x*exp(6*x). - _Michael Somos_, Dec 16 2019

%F From _Amiram Eldar_, Oct 28 2020: (Start)

%F Sum_{n>=1} 1/a(n) = 6*log(6/5).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(7/6). (End)

%e G.f. = x + 12*x^2 + 108*x^3 + 864*x^4 + 6480*x^5 + 46656*x^6 + ... - _Michael Somos_, Dec 16 2019

%t f[n_]:=n*6^(n-1);f[Range[40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011 *)

%t LinearRecurrence[{12,-36},{1,12},20] (* _Harvey P. Dale_, Apr 28 2015 *)

%o (Sage) [lucas_number1(n,12,36) for n in range(1, 21)] # _Zerinvary Lajos_, Apr 28 2009

%o (Magma) [n*(6^(n-1)): n in [1..30]]; // _Vincenzo Librandi_, Jun 09 2011

%o (PARI) a(n)=n*6^(n-1) \\ _Charles R Greathouse IV_, Oct 07 2015

%Y Cf. A002697, A027471.

%K easy,nonn

%O 1,2

%A _Barry E. Williams_, Jan 13 2000

%E More terms from _James A. Sellers_, Feb 02 2000

%E More terms from _Zerinvary Lajos_, Oct 02 2007