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%I #39 May 08 2023 09:35:15
%S 1,27,405,5103,59049,649539,6908733,71744535,731794257,7360989291,
%T 73222472421,721764371007,7060738412025,68630377364883,
%U 663426981193869,6382625094934119,61149666232110753,583701359488329915,5553501505988967477,52683216989246691471,498464283821334080841
%N a(n) = (2*n + 1)*9^n.
%H Vincenzo Librandi, <a href="/A155988/b155988.txt">Table of n, a(n) for n = 0..200</a>
%H David H. Bailey, <a href="https://www.davidhbailey.com/dhbpapers/bbp-formulas.pdf">A Compendium of BBP-Type Formulas for Mathematical Constants</a>, 2017, page 14. [From _Jaume Oliver Lafont_, Sep 25 2009]
%H Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Log2/log2Formulas.html">Collection of formulas for log 2</a>.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).
%F G.f.: (1 + 9*x)/(1 - 9*x)^2.
%F a(n) = 18*a(n-1) - 81*a(n-2) for n>=2.
%F Sum_{n>=0} 1/a(n) = (3/2)*log(2).
%F a(n) = A005408(n) * A001019(n).
%F a(n) = (2*n - 1)*3^(2*n-1)/3 = A060851(n)/3.
%F Sum_{n>=0} (-1)^n/a(n) = 3*arctan(1/3). - _Amiram Eldar_, Feb 26 2022
%F E.g.f.: exp(9*x)*(1 + 18*x). - _Stefano Spezia_, May 07 2023
%o (PARI) a(n)=(2*n+1)*9^n;
%o (Magma) [(2*n+1)*9^n: n in [0..20]]; // _Vincenzo Librandi_, Jun 08 2011
%o (Maxima) makelist((2*n+1)*9^n, n, 0, 20); /* _Martin Ettl_, Nov 11 2012 */
%Y Cf. A058962 for the similar (2n+1)4^n.
%Y Cf. A001019, A005408, A060851, A096949, A096950, A154920, A164985, A165132.
%K nonn,easy
%O 0,2
%A _Jaume Oliver Lafont_, Feb 01 2009
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