A006091 a(n) = n^n - n + 1. (Formerly M3111)

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

Offset

1,2

Comments

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

Also main diagonal of A193871. - Omar E. Pol, Aug 22 2011

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.

Formula

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

Mathematica

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

Prog

(Magma) [n^n - n + 1: n in [1..20]]; // Vincenzo Librandi, Aug 23 2011
(PARI) A006091(n)=n^n-n+1 \\ M. F. Hasler, Oct 30 2017

Crossrefs

Cf. A014293.

Sequence in context: A260209 A086655 A064326 * A357232 A355865 A009042

Adjacent sequences: A006088 A006089 A006090 * A006092 A006093 A006094

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved