A008786 a(n) = (n+5)^n.

1, 6, 49, 512, 6561, 100000, 1771561, 35831808, 815730721, 20661046784, 576650390625, 17592186044416, 582622237229761, 20822964865671168, 799006685782884121, 32768000000000000000, 1430568690241985328321, 66249952919459433152512, 3244150909895248285300369

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200

Crossrefs

Cf. A000169, A000272, A000312, A007778, A007830, A008785, this sequence, A008787, A008788, A008789, A008790, A008791.

Programs

GAP

List([0..20], n-> (n+5)^n); # G. C. Greubel, Sep 11 2019

Magma

[(n+5)^n: n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

Mathematica

Table[(n+5)^n,{n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

PARI

vector(20, n, (n+4)^(n-1)) \\ G. C. Greubel, Sep 11 2019

Sage

[(n+5)^n for n in (0..20)] # G. C. Greubel, Sep 11 2019

Formula

E.g.f.(x) for b(n) = n^(n-5) = a(n-5): T - (15/16)*T^2 + (85/216)T^3 - (25/288)*T^4 + (1/120)*T^5, where T=T(x) is Euler's tree function. - Len Smiley, Nov 17 2001

E.g.f.: LambertW(-x)^5/((-x)^5*(1+LambertW(-x))). - Vladeta Jovovic, Nov 07 2003

E.g.f.: (1/4)*d/dx((LambertW(-x)/(-x))^4). - Wolfdieter Lang, Oct 25 2022