A062023 a(n) = (n^(n+1) + n^(n-1))/2.

1, 5, 45, 544, 8125, 143856, 2941225, 68157440, 1764915561, 50500000000, 1582182900661, 53868106874880, 1980337235410885, 78180905165533184, 3298800640869140625, 148150413341979836416, 7055872821971695929745, 355210628457538186444800

Offset: 1

Author

Amarnath Murthy, Jun 02 2001

Keywords

• nonn

Comments

a(n) is the number of monotonic runs over all length n words on an alphabet of n letters. - Geoffrey Critzer, Jun 25 2013

Examples

			a(3) = {3^4 +3^2}/2 = 45.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..100

Crossrefs

Cf. A229078.

Programs

Mathematica

Table[(n^(n-1)+n^(n+1))/2,{n,1,20}] (* Geoffrey Critzer, Jun 25 2013 *)

PARI

a(n) = { (n^(n+1) + n^(n-1))/2 } \\ Harry J. Smith, Jul 29 2009

SageMath

[(n^(n+1) + n^(n-1))/2 for n in (1..20)] # G. C. Greubel, May 04 2022

Formula

E.g.f.: (-1/2)*LambertW(-x)*(1 + 1/(1 + LambertW(-x))^3). - G. C. Greubel, May 04 2022

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jun 06 2001