A008790 a(n) = n^(n+4).

0, 1, 64, 2187, 65536, 1953125, 60466176, 1977326743, 68719476736, 2541865828329, 100000000000000, 4177248169415651, 184884258895036416, 8650415919381337933, 426878854210636742656, 22168378200531005859375

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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, A008788, A008789, A008791.

Programs

GAP

List([0..20], n-> n^(n+4)); # G. C. Greubel, Sep 11 2019

Magma

[n^(n+4): n in [0..20]]; // Vincenzo Librandi, Jun 11 2013

Maple

a:=n->mul(n,k=-3..n):seq(a(n),n=0..20); # Zerinvary Lajos, Jan 26 2008

Mathematica

Table[n^(n+4),{n,0,20}](* Vladimir Joseph Stephan Orlovsky, Dec 26 2010 *)

PARI

vector(20, n, (n-1)^(n+3)) \\ G. C. Greubel, Sep 11 2019

Sage

[n^(n+4) for n in (0..20)] # G. C. Greubel, Sep 11 2019

Formula

E.g.f.: T*(1 +22*T +58*T^2 +24*T^3)*(1-T)^(-9); where T is Euler's tree function (see A000169). - Len Smiley, Nov 17 2001

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

E.g.f.: d^4/dx^4 {x^4/(T(x)^4*(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