A060072 a(n) = (n^(n-1) - 1)/(n-1) for n>1, a(1) = 0.

0, 1, 4, 21, 156, 1555, 19608, 299593, 5380840, 111111111, 2593742460, 67546215517, 1941507093540, 61054982558011, 2085209001813616, 76861433640456465, 3041324492229179280, 128583032925805678351, 5784852794328402307380, 275941052631578947368421

Offset: 1

Author

Henry Bottomley, Feb 21 2001

Keywords

• nonn

Comments

(n-1)-digit repunits in base n written in decimal.

Examples

			a(10)=111111111; i.e., just nine 1's (converted from base 10 to decimal).
		

Links

• Harry J. Smith, Table of n, a(n) for n=1..200

Crossrefs

Cf. A000169, A037205, A055869, A060073, A125118, A228275.

Cf. other sequences of generalized repunits, such as A053696, A055129, A031973, A125598, A173468, A023037, A119598, A085104, and A162861.

Programs

Magma

[0] cat [ (n^(n-1) -1)/(n-1) : n in [2..25]]; // G. C. Greubel, Aug 15 2022

Mathematica

Join[{0},Array[(#^(#-1)-1)/(#-1)&,20,2]] (* Harvey P. Dale, Jun 04 2013 *)

PARI

a(n) = if (n==1, 0, (n^(n - 1) - 1)/(n - 1)); \\ Harry J. Smith, Jul 01 2009

SageMath

[0]+[(n^(n-1) -1)/(n-1) for n in (2..25)] # G. C. Greubel, Aug 15 2022

Formula

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]

a(n) = Sum_{j=2..n} n^(n-j). - Zerinvary Lajos, Sep 11 2006

a(n+1) = A125118(n,n). - Reinhard Zumkeller, Nov 21 2006

a(n) = Integral_{x=1/n..1} 1/x^n dx. - Francesco Daddi, Aug 01 2011

a(n) = A037205(n-1)/(n-1) = A060073(n)*(n-1) = A023037(n) - A000169(n).

a(n) = [x^n] x^2/((1 - x)*(1 - n*x)). - Ilya Gutkovskiy, Oct 04 2017

a(n) = 1 + A228275(n, n-2) for n >= 2. - Mathew Englander, Dec 14 2020

Extensions

Name edited by Michel Marcus, Dec 14 2020