A155988 a(n) = (2*n + 1)*9^n.
1, 27, 405, 5103, 59049, 649539, 6908733, 71744535, 731794257, 7360989291, 73222472421, 721764371007, 7060738412025, 68630377364883, 663426981193869, 6382625094934119, 61149666232110753, 583701359488329915, 5553501505988967477, 52683216989246691471, 498464283821334080841
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- David H. Bailey, A Compendium of BBP-Type Formulas for Mathematical Constants, 2017, page 14.
- Xavier Gourdon and Pascal Sebah, Collection of formulas for log 2.
- Index entries for linear recurrences with constant coefficients, signature (18,-81).
Crossrefs
Programs
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Magma
[(2*n+1)*9^n: n in [0..20]]; // Vincenzo Librandi, Jun 08 2011
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Maxima
makelist((2*n+1)*9^n, n, 0, 20); /* Martin Ettl, Nov 11 2012 */
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PARI
a(n)=(2*n+1)*9^n;
Formula
G.f.: (1 + 9*x)/(1 - 9*x)^2.
a(n) = 18*a(n-1) - 81*a(n-2) for n>=2.
Sum_{n>=0} 1/a(n) = (3/2)*log(2).
a(n) = (2*n - 1)*3^(2*n-1)/3 = A060851(n)/3.
Sum_{n>=0} (-1)^n/a(n) = 3*arctan(1/3). - Amiram Eldar, Feb 26 2022
E.g.f.: exp(9*x)*(1 + 18*x). - Stefano Spezia, May 07 2023
Comments