A016175 Expansion of 1/((1-6x)(1-12x)).

1, 18, 252, 3240, 40176, 489888, 5925312, 71383680, 858283776, 10309483008, 123774262272, 1485653944320, 17830024114176, 213973350064128, 2567758564933632, 30813572964188160, 369765696680165376

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (18,-72).

Formula

a(n) = (6^n)*Stirling2(n+2, 2), n >= 0, with Stirling2(n, m) = A008277(n, m).

a(n) = -6^n + 2*12^n.

E.g.f.: (d^2/dx^2)((((exp(6*x)-1)/6)^2)/2!) = -exp(6*x) + 2*exp(12*x).

a(n-1) = ((9+sqrt9)^n - (9-sqrt9)^n)/6. - Al Hakanson (hawkuu(AT)gmail.com), Jan 07 2009

a(n) = 12*a(n-1) + 6^n, n >= 1. - Vincenzo Librandi, Feb 09 2011

a(n) = 18*a(n-1) - 72*a(n-2), n >= 2. - Vincenzo Librandi, Feb 09 2011

Mathematica

Join[{a=1, b=18}, Table[c=18*b-72*a; a=b; b=c, {n, 40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011 *)
LinearRecurrence[{18, -72}, {1, 18}, 20] (* Harvey P. Dale, Nov 25 2013 *)

Prog

(PARI) Vec(1/((1-6*x)*(1-12*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Second column of triangle A075501.

Cf. A075916.

Sequence in context: A088924 A125475 A255371 * A062141 A157708 A159537

Adjacent sequences: A016172 A016173 A016174 * A016176 A016177 A016178

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved