A376765 a(n) = (1/2)*Sum_{k=0..n} n^binomial(n,k).

0, 1, 4, 30, 2308, 9768755, 1828549405062726, 378818692266223327546801733500, 822752278660977165496641302425735395827886114383655917217382408, 1716153733051169540307898602341497569311487178262131715007420471535292324238528850823190109780802970900137357654221203141

Offset: 0

Author

N. J. A. Sloane, Nov 02 2024

Keywords

• nonn

Comments

For n>0, this is one-half of (one possible definition of) the number of partial maps from an n-set to itself.

Crossrefs

Cf. A000312, A007840, A376766.

Programs

Mathematica

Table[Sum[n^Binomial[n,k],{k,0,n}]/2,{n,0,9}] (* James C. McMahon, Nov 03 2024 *)

Python

from math import comb
def A376765(n): return sum(n**comb(n,k) for k in range(n+1))>>1 # Chai Wah Wu, Nov 03 2024

Extensions

a(9) from James C. McMahon, Nov 03 2024