%I #15 Oct 25 2025 13:56:42

%S 1,27,567,10935,203391,3720087,67493007,1219657095,21996874431,

%T 396331160247,7137447668847,128505439098855,2313380333315871,

%U 41643387865514007,749603858371707087,13493075341822822215,242877209172999651711,4371806442295693397367,78692666055957778151727

%N Second column of triangle A075504.

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

%H Michael De Vlieger, <a href="/A076008/b076008.txt">Table of n, a(n) for n = 0..796</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (27,-162).

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

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

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

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

%F a(0)=1, a(1)=27, a(n) = 27*a(n-1) - 162*a(n-2). - _Harvey P. Dale_, Dec 01 2015

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

%Y Cf. A001019, A076009.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Oct 02 2002