A006091 a(n) = n^n - n + 1.

1, 3, 25, 253, 3121, 46651, 823537, 16777209, 387420481, 9999999991, 285311670601, 8916100448245, 302875106592241, 11112006825558003, 437893890380859361, 18446744073709551601, 827240261886336764161, 39346408075296537575407, 1978419655660313589123961

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Related to famous "coconuts" problem - cf. A002021, A002022.

References

• Archimedeans Problems Drive, Eureka, 41 (1981), 7.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• Archimedeans Problems Drive, Problems for 1980, Eureka, 41 (1981), 6-7. (Annotated scanned copy)
• J. Burkardt, The Coconut puzzle (version 3)
• Santo D'Agostino, "The Coconut Problem"; Updated With Solution, May 2011.
• Mark Richardson, A Needlessly Complicated and Unhelpful Solution to Ben Ames Williams' Famous Coconuts Problem, The Winnower, Authorea (2016) Vol. 3.

Crossrefs

Cf. A014293.

Programs

Magma

[n^n - n + 1: n in [1..20]]; // Vincenzo Librandi, Aug 23 2011

Mathematica

Table[n^n-n+1,{n,20}] (* Harvey P. Dale, Jun 09 2011 *)

PARI

A006091(n)=n^n-n+1 \\ M. F. Hasler, Oct 30 2017

Formula

E.g.f.: 1/(1 + LambertW(-x)) + exp(x)*(1 - x) - 2. - Ilya Gutkovskiy, Oct 30 2017