A008791 a(n) = n^(n+5).

0, 1, 128, 6561, 262144, 9765625, 362797056, 13841287201, 549755813888, 22876792454961, 1000000000000000, 45949729863572161, 2218611106740436992, 112455406951957393129, 5976303958948914397184, 332525673007965087890625

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, A008790.

Programs

GAP

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

Magma

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

Maple

a:=n->mul( n, k=-4..n): seq(a(n), n=0..20); # Zerinvary Lajos, Jan 26 2008

Mathematica

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

PARI

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

Sage

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

Formula

E.g.f.(x): T*(1 + 52*T + 328*T^2 + 444*T^3 + 120*T^4)*(1-T)^(-11); 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 diagonals of A048993. - Tom Copeland, Oct 03 2011

E.g.f.: d^5/dx^5 {x^5/(T(x)^5*(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