A076008 Second column of triangle A075504.

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

Offset: 0

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A001019, A076009.

Programs

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 *)

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