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

1, 12, 108, 864, 6480, 46656, 326592, 2239488, 15116544, 100776960, 665127936, 4353564672, 28298170368, 182849716224, 1175462461440, 7522959753216, 47958868426752, 304679870005248, 1929639176699904, 12187194800209920, 76779327241322496, 482612914088312832

Offset: 1

Author

Barry E. Williams, Jan 13 2000

Keywords

• easy
• nonn

Comments

Binomial transform of A053464. - R. J. Mathar, Oct 26 2011

Examples

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

References

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

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..400
• Frank Ellermann, Illustration of binomial transforms.
• Index entries for linear recurrences with constant coefficients, signature (12,-36).

Crossrefs

Cf. A002697, A027471.

Programs

Magma

[n*(6^(n-1)): n in [1..30]]; // Vincenzo Librandi, Jun 09 2011

Mathematica

f[n_]:=n*6^(n-1);f[Range[40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{12,-36},{1,12},20] (* Harvey P. Dale, Apr 28 2015 *)

PARI

a(n)=n*6^(n-1) \\ Charles R Greathouse IV, Oct 07 2015

Sage

[lucas_number1(n,12,36) for n in range(1, 21)] # Zerinvary Lajos, Apr 28 2009

Formula

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

G.f.: x/(6x-1)^2. - Zerinvary Lajos, Apr 28 2009

E.g.f.: x*exp(6*x). - Michael Somos, Dec 16 2019

From Amiram Eldar, Oct 28 2020: (Start)

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

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

Extensions

More terms from James Sellers, Feb 02 2000

More terms from Zerinvary Lajos, Oct 02 2007