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A053469 a(n) = n*6^(n-1).

%I A053469 #57 Jul 02 2025 16:01:59
%S A053469 1,12,108,864,6480,46656,326592,2239488,15116544,100776960,665127936,
%T A053469 4353564672,28298170368,182849716224,1175462461440,7522959753216,
%U A053469 47958868426752,304679870005248,1929639176699904,12187194800209920,76779327241322496,482612914088312832
%N A053469 a(n) = n*6^(n-1).
%C A053469 Binomial transform of A053464. - _R. J. Mathar_, Oct 26 2011
%D A053469 A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H A053469 Vincenzo Librandi, <a href="/A053469/b053469.txt">Table of n, a(n) for n = 1..400</a>
%H A053469 Frank Ellermann, <a href="/A001792/a001792.txt">Illustration of binomial transforms</a>.
%H A053469 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-36).
%F A053469 a(n) = 12*a(n-1) - 36*a(n-2), n>=3.
%F A053469 G.f.: x/(6x-1)^2. - _Zerinvary Lajos_, Apr 28 2009
%F A053469 E.g.f.: x*exp(6*x). - _Michael Somos_, Dec 16 2019
%F A053469 From _Amiram Eldar_, Oct 28 2020: (Start)
%F A053469 Sum_{n>=1} 1/a(n) = 6*log(6/5).
%F A053469 Sum_{n>=1} (-1)^(n+1)/a(n) = 6*log(7/6). (End)
%e A053469 G.f. = x + 12*x^2 + 108*x^3 + 864*x^4 + 6480*x^5 + 46656*x^6 + ... - _Michael Somos_, Dec 16 2019
%t A053469 f[n_]:=n*6^(n-1);f[Range[40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011 *)
%t A053469 LinearRecurrence[{12,-36},{1,12},20] (* _Harvey P. Dale_, Apr 28 2015 *)
%o A053469 (Sage) [lucas_number1(n,12,36) for n in range(1, 21)] # _Zerinvary Lajos_, Apr 28 2009
%o A053469 (Magma) [n*(6^(n-1)): n in [1..30]]; // _Vincenzo Librandi_, Jun 09 2011
%o A053469 (PARI) a(n)=n*6^(n-1) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A053469 Cf. A002697, A027471.
%K A053469 easy,nonn
%O A053469 1,2
%A A053469 _Barry E. Williams_, Jan 13 2000
%E A053469 More terms from _James Sellers_, Feb 02 2000
%E A053469 More terms from _Zerinvary Lajos_, Oct 02 2007