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

1,2

Comments

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

By symmetry, counts a lot of other simple classes of endofunctions.

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A076014.

A diagonal of array A103438.

A subset of A000312.

Sequence in context: A140963 A284759 A284760 * A004659 A054202 A084420

Adjacent sequences: A076012 A076013 A076014 * A076016 A076017 A076018

Keyword

nonn,easy

Author

Wolfdieter Lang, Oct 02 2002

Extensions

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

Status

approved