A076008 Second column of triangle A075504.

1, 27, 567, 10935, 203391, 3720087, 67493007, 1219657095, 21996874431, 396331160247, 7137447668847, 128505439098855, 2313380333315871, 41643387865514007, 749603858371707087, 13493075341822822215

Offset

0,2

Comments

The e.g.f. given below is Sum_{m=0..1} (A075513(3,m)*exp(9*(m+1)*x)).

Links

Michael De Vlieger, Table of n, a(n) for n = 0..796

Index entries for linear recurrences with constant coefficients, signature (27,-162).

Formula

a(n) = A075504(n+2, 2) = (9^n)*S2(n+2, 2) with S2(n, m) := A008277(n, m) (Stirling2).

a(n) = -9^n + 2*18^n.

G.f.: 1/((1-9*x)*(1-18*x)).

E.g.f.: (d^2/dx^2)(((exp(9*x)-1)/9)^2)/2! = -exp(9*x) + 2*exp(18*x).

a(0)=1, a(1)=27, a(n) = 27*a(n-1) - 162*a(n-2). - Harvey P. Dale, Dec 01 2015

Mathematica

CoefficientList[Series[1/((1-9x)(1-18x)), {x, 0, 30}], x] (* or *) LinearRecurrence[{27, -162}, {1, 27}, 30] (* Harvey P. Dale, Dec 01 2015 *)

Crossrefs

Cf. A001019, A076009.

Sequence in context: A347591 A267544 A061914 * A232944 A185891 A185883

Adjacent sequences: A076005 A076006 A076007 * A076009 A076010 A076011

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Status

approved