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.
%I A016135 #40 Mar 16 2025 16:05:15 %S A016135 1,13,147,1625,17891,196833,2165227,23817625,261994131,2881935953, %T A016135 31701296507,348714263625,3835856903971,42194425951873, %U A016135 464138685486987,5105525540389625,56160780944351411,617768590387996593,6795454494268224667,74749999436950995625,822249993806462000451 %N A016135 Expansion of g.f. 1/((1-2*x)*(1-11*x)). %H A016135 Vincenzo Librandi, <a href="/A016135/b016135.txt">Table of n, a(n) for n = 0..300</a> %H A016135 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (13,-22). %F A016135 a(n) = (11^(n+1) - 2^(n+1))/9. - _Zerinvary Lajos_, Jun 05 2009 %F A016135 a(n) = 13*a(n-1) - 22*a(n-2). - _Vincenzo Librandi_, Jun 02 2011 %F A016135 From _Elmo R. Oliveira_, Mar 08 2025: (Start) %F A016135 E.g.f.: exp(2*x)*(11*exp(9*x) - 2)/9. %F A016135 a(n) = A139740(n+1)/9. (End) %t A016135 LinearRecurrence[{13,-22},{1,13},30] (* or *) CoefficientList[Series[ 1/((1-2x)*(1-11x)),{x,0,30}],x] (* _Harvey P. Dale_, Oct 15 2011 *) %o A016135 (Sage) [(11^(n+1) - 2^(n+1))/9 for n in range(0,20)] # _Zerinvary Lajos_, Jun 05 2009 %o A016135 (PARI) a(n)=(11^n++-2^n)/9 \\ _Charles R Greathouse IV_, Mar 26 2012 %Y A016135 Cf. A139740. %K A016135 nonn,easy %O A016135 0,2 %A A016135 _N. J. A. Sloane_ %E A016135 Incorrect comment removed by _Charles R Greathouse IV_, Mar 26 2012