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A053422 n times (n 1's): a(n) = n*(10^n - 1)/9.

%I A053422 #34 Sep 14 2023 06:20:11
%S A053422 0,1,22,333,4444,55555,666666,7777777,88888888,999999999,11111111110,
%T A053422 122222222221,1333333333332,14444444444443,155555555555554,
%U A053422 1666666666666665,17777777777777776,188888888888888887,1999999999999999998,21111111111111111109,222222222222222222220,2333333333333333333331
%N A053422 n times (n 1's): a(n) = n*(10^n - 1)/9.
%C A053422 R_a(n) is the least repunit divisible by the square of R_n = (10^n - 1)/9. - _Lekraj Beedassy_, Jun 07 2006
%H A053422 G. C. Greubel, <a href="/A053422/b053422.txt">Table of n, a(n) for n = 0..995</a>
%H A053422 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (22,-141,220,-100).
%F A053422 a(n) = n*A002275(n) = a(n-1)*10n/(n-1) + n.
%F A053422 O.g.f.: x*(1-10*x^2)/((1-x)^2*(1-10*x)^2). - _R. J. Mathar_, Jan 21 2008
%F A053422 E.g.f.: x*exp(x)*(10*exp(9*x) - 1)/9. - _Stefano Spezia_, Sep 14 2023
%t A053422 LinearRecurrence[{22,-141,220,-100}, {0, 1, 22, 333}, 50] (* _G. C. Greubel_, May 25 2018 *)
%t A053422 CoefficientList[Series[x (1-10x^2)/((1-x)^2(1-10x)^2),{x,0,30}],x] (* _Harvey P. Dale_, Jun 29 2021 *)
%o A053422 (Sage) [gaussian_binomial(n,1,10)*n for n in range(0,22)] # _Zerinvary Lajos_, May 29 2009
%o A053422 (PARI) x='x+O('x^30); concat([0], Vec(x*(1-10*x^2)/((1-x)^2*(1-10*x)^2))) \\ _G. C. Greubel_, May 25 2018
%o A053422 (Magma) I:=[0, 1, 22, 333]; [n le 4 select I[n] else 22*Self(n-1) - 141*Self(n-2) +220*Self(n-3) -100*Self(n-4): n in [1..30]]; // _G. C. Greubel_, May 25 2018
%Y A053422 Cf. A000461, A002275, A048376.
%K A053422 base,easy,nonn
%O A053422 0,3
%A A053422 _Henry Bottomley_, Mar 07 2000
%E A053422 Corrected by _Jason Earls_, Sep 02 2006