A008788 a(n) = n^(n+2).

0, 1, 16, 243, 4096, 78125, 1679616, 40353607, 1073741824, 31381059609, 1000000000000, 34522712143931, 1283918464548864, 51185893014090757, 2177953337809371136, 98526125335693359375, 4722366482869645213696

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Examples

			G.f. = x + 16*x^2 + 243*x^3 + 4096*x^4 + 78125*x^5 + 1679616*x^6 + ...
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Crossrefs

Cf. A000169, A000272, A000312, A007778, A007830, A008785, A008786, A008787, A008789, A008790, A008791.

Programs

GAP

List([0..20], n-> n^(n+2)); # G. C. Greubel, Sep 11 2019

Magma

[n^(n+2): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

Mathematica

Table[n^(n+2), {n,0,20}] (* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)
CoefficientList[Series[LambertW[-x] * (2*LambertW[-x]-1) / (1 + LambertW[-x])^5, {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Dec 20 2014 *)

PARI

vector(20, n, (n-1)^(n+1)) \\ G. C. Greubel, Nov 14 2017

Sage

[n^(n+2) for n in (0..20)] # G. C. Greubel, Sep 11 2019

Formula

E.g.f.(x): T*(1 + 2*T)*(1-T)^(-5); where T=T(x) is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001

See A008517 and A134991 for similar e.g.f.s. and A048993. - Tom Copeland, Oct 03 2011

E.g.f.: d^2/dx^2 {x^2/(T(x)^2*(1-T(x)))}, where T(x) = Sum_{n>=1} n^(n-1)*x^n/n! is the tree function of A000169. - Peter Bala, Aug 05 2012