A076015 Sum of the (n-1)-th powers of the first n integers.

1, 3, 14, 100, 979, 12201, 184820, 3297456, 67731333, 1574304985, 40851766526, 1170684360924, 36720042483591, 1251308658130545, 46034015337733480, 1818399978159990976, 76762718946972480009

Offset: 1

Author

Wolfdieter Lang, Oct 02 2002

Keywords

• nonn
• easy

Comments

a(n) is the number of length n sequences of [n] that start with their maximum value.

By symmetry, counts many other simple classes of endofunctions.

Examples

			The 3 sequences for n=2 are 11, 21, 22.
The 14 = 3^0 + 3^1 + 3^2 sequences starting with their maximum value for n=3 are 111, 211, 212, 221, 222, 311, 312, 313, 321, 322, 323, 331, 332, 333.
		

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..387

Crossrefs

Cf. A076014.

A diagonal of array A103438.

A subset of A000312.

Programs

Maple

a:=n->sum((n-j+1)^n,j=0..n): seq(a(n), n=0..17); # Zerinvary Lajos, Jun 05 2008

Mathematica

f[n_]:=Module[{s=0},Do[s+=a^n,{a,0,n+1}]; s]; Table[f[n],{n,20}] (* Vladimir Joseph Stephan Orlovsky, Feb 18 2010 *)
Table[Sum[m^(n-1),{m,n}],{n,20}] (* Harvey P. Dale, Jan 26 2016 *)

PARI

vector(20, n, sum(m=1, n, m^(n-1))) \\ Michel Marcus, Jan 14 2015

Formula

a(n) = Sum_{m=1..n} m^(n-1), n >= 1.

Extensions

Definition changed and example added by Olivier Gérard, Jan 28 2023