cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A076008 Second column of triangle A075504.

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%I A076008 #12 Dec 25 2017 04:01:38
%S A076008 1,27,567,10935,203391,3720087,67493007,1219657095,21996874431,
%T A076008 396331160247,7137447668847,128505439098855,2313380333315871,
%U A076008 41643387865514007,749603858371707087,13493075341822822215
%N A076008 Second column of triangle A075504.
%C A076008 The e.g.f. given below is Sum_{m=0..1} (A075513(3,m)*exp(9*(m+1)*x)).
%H A076008 Michael De Vlieger, <a href="/A076008/b076008.txt">Table of n, a(n) for n = 0..796</a>
%H A076008 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (27,-162).
%F A076008 a(n) = A075504(n+2, 2) = (9^n)*S2(n+2, 2) with S2(n, m) := A008277(n, m) (Stirling2).
%F A076008 a(n) = -9^n + 2*18^n.
%F A076008 G.f.: 1/((1-9*x)*(1-18*x)).
%F A076008 E.g.f.: (d^2/dx^2)(((exp(9*x)-1)/9)^2)/2! = -exp(9*x) + 2*exp(18*x).
%F A076008 a(0)=1, a(1)=27, a(n) = 27*a(n-1) - 162*a(n-2). - _Harvey P. Dale_, Dec 01 2015
%t A076008 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 A076008 Cf. A001019, A076009.
%K A076008 nonn,easy
%O A076008 0,2
%A A076008 _Wolfdieter Lang_, Oct 02 2002