A081127 11th binomial transform of (0,1,0,0,0,0,0,...).
0, 1, 22, 363, 5324, 73205, 966306, 12400927, 155897368, 1929229929, 23579476910, 285311670611, 3423740047332, 40799568897373, 483317970015034, 5696247503748615, 66835970710650416, 781145407680726737
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (22,-121).
Programs
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Magma
[n*11^(n-1): n in [0..30]]; // Vincenzo Librandi, Jun 06 2011
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Mathematica
a[n_]:=n*11^(n-1); a[Range[0,40]] (* Vladimir Joseph Stephan Orlovsky, Feb 09 2011*)
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SageMath
[11^(n-1)*n for n in range(31)] # G. C. Greubel, Jan 16 2024
Formula
a(n) = 22*a(n-1) - 121*a(n-2), with a(0)=0, a(1)=1.
a(n) = n*11^(n-1).
G.f.: x/(1-11*x)^2.
a(n) = A003415(11^n). - Bruno Berselli, Oct 22 2013
From Amiram Eldar, Oct 28 2020: (Start)
Sum_{n>=1} 1/a(n) = 11*log(11/10).
Sum_{n>=1} (-1)^(n+1)/a(n) = 11*log(12/11). (End)
E.g.f.: x*exp(11*x). - G. C. Greubel, Jan 16 2024