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%I #57 Aug 15 2022 04:25:26
%S 0,1,4,21,156,1555,19608,299593,5380840,111111111,2593742460,
%T 67546215517,1941507093540,61054982558011,2085209001813616,
%U 76861433640456465,3041324492229179280,128583032925805678351,5784852794328402307380,275941052631578947368421
%N a(n) = (n^(n-1) - 1)/(n-1) for n>1, a(1) = 0.
%C (n-1)-digit repunits in base n written in decimal.
%H Harry J. Smith, <a href="/A060072/b060072.txt">Table of n, a(n) for n=1..200</a>
%F a(n+1) = Sum_{k=1..n} n^(k-1)*C(n, k). - _Olivier Gérard_, Jun 26 2001 [Corrected by _Mathew Englander_, Dec 15 2020]
%F a(n) = Sum_{j=2..n} n^(n-j). - _Zerinvary Lajos_, Sep 11 2006
%F a(n+1) = A125118(n,n). - _Reinhard Zumkeller_, Nov 21 2006
%F a(n) = Integral_{x=1/n..1} 1/x^n dx. - _Francesco Daddi_, Aug 01 2011
%F a(n) = A037205(n-1)/(n-1) = A060073(n)*(n-1) = A023037(n) - A000169(n).
%F a(n) = [x^n] x^2/((1 - x)*(1 - n*x)). - _Ilya Gutkovskiy_, Oct 04 2017
%F a(n) = 1 + A228275(n, n-2) for n >= 2. - _Mathew Englander_, Dec 14 2020
%e a(10)=111111111; i.e., just nine 1's (converted from base 10 to decimal).
%t Join[{0},Array[(#^(#-1)-1)/(#-1)&,20,2]] (* _Harvey P. Dale_, Jun 04 2013 *)
%o (PARI) a(n) = if (n==1, 0, (n^(n - 1) - 1)/(n - 1)); \\ _Harry J. Smith_, Jul 01 2009
%o (Magma) [0] cat [ (n^(n-1) -1)/(n-1) : n in [2..25]]; // _G. C. Greubel_, Aug 15 2022
%o (SageMath) [0]+[(n^(n-1) -1)/(n-1) for n in (2..25)] # _G. C. Greubel_, Aug 15 2022
%Y Cf. A000169, A037205, A055869, A060073, A125118, A228275.
%Y Cf. other sequences of generalized repunits, such as A053696, A055129, A031973, A125598, A173468, A023037, A119598, A085104, and A162861.
%K nonn
%O 1,3
%A _Henry Bottomley_, Feb 21 2001
%E Name edited by _Michel Marcus_, Dec 14 2020
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