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A081127 11th binomial transform of (0,1,0,0,0,0,0,...).

%I A081127 #28 Jan 17 2024 01:14:02
%S A081127 0,1,22,363,5324,73205,966306,12400927,155897368,1929229929,
%T A081127 23579476910,285311670611,3423740047332,40799568897373,
%U A081127 483317970015034,5696247503748615,66835970710650416,781145407680726737
%N A081127 11th binomial transform of (0,1,0,0,0,0,0,...).
%H A081127 Vincenzo Librandi, <a href="/A081127/b081127.txt">Table of n, a(n) for n = 0..200</a>
%H A081127 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (22,-121).
%F A081127 a(n) = 22*a(n-1) - 121*a(n-2), with a(0)=0, a(1)=1.
%F A081127 a(n) = n*11^(n-1).
%F A081127 G.f.: x/(1-11*x)^2.
%F A081127 a(n) = A003415(11^n). - _Bruno Berselli_, Oct 22 2013
%F A081127 From _Amiram Eldar_, Oct 28 2020: (Start)
%F A081127 Sum_{n>=1} 1/a(n) = 11*log(11/10).
%F A081127 Sum_{n>=1} (-1)^(n+1)/a(n) = 11*log(12/11). (End)
%F A081127 E.g.f.: x*exp(11*x). - _G. C. Greubel_, Jan 16 2024
%t A081127 a[n_]:=n*11^(n-1); a[Range[0,40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011*)
%o A081127 (Magma) [n*11^(n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 06 2011
%o A081127 (SageMath) [11^(n-1)*n for n in range(31)] # _G. C. Greubel_, Jan 16 2024
%Y A081127 Cf. A003415, A038315, A053541, A081128.
%K A081127 easy,nonn
%O A081127 0,3
%A A081127 _Paul Barry_, Mar 07 2003