%I #28 Jan 17 2024 01:14:02

%S 0,1,22,363,5324,73205,966306,12400927,155897368,1929229929,

%T 23579476910,285311670611,3423740047332,40799568897373,

%U 483317970015034,5696247503748615,66835970710650416,781145407680726737

%N 11th binomial transform of (0,1,0,0,0,0,0,...).

%H Vincenzo Librandi, <a href="/A081127/b081127.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (22,-121).

%F a(n) = 22*a(n-1) - 121*a(n-2), with a(0)=0, a(1)=1.

%F a(n) = n*11^(n-1).

%F G.f.: x/(1-11*x)^2.

%F a(n) = A003415(11^n). - _Bruno Berselli_, Oct 22 2013

%F From _Amiram Eldar_, Oct 28 2020: (Start)

%F Sum_{n>=1} 1/a(n) = 11*log(11/10).

%F Sum_{n>=1} (-1)^(n+1)/a(n) = 11*log(12/11). (End)

%F E.g.f.: x*exp(11*x). - _G. C. Greubel_, Jan 16 2024

%t a[n_]:=n*11^(n-1); a[Range[0,40]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 09 2011*)

%o (Magma) [n*11^(n-1): n in [0..30]]; // _Vincenzo Librandi_, Jun 06 2011

%o (SageMath) [11^(n-1)*n for n in range(31)] # _G. C. Greubel_, Jan 16 2024

%Y Cf. A003415, A038315, A053541, A081128.

%K easy,nonn

%O 0,3

%A _Paul Barry_, Mar 07 2003