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A376765
a(n) = (1/2)*Sum_{k=0..n} n^binomial(n,k).
2
0, 1, 4, 30, 2308, 9768755, 1828549405062726, 378818692266223327546801733500, 822752278660977165496641302425735395827886114383655917217382408, 1716153733051169540307898602341497569311487178262131715007420471535292324238528850823190109780802970900137357654221203141
OFFSET
0,3
COMMENTS
For n>0, this is one-half of (one possible definition of) the number of partial maps from an n-set to itself.
MATHEMATICA
Table[Sum[n^Binomial[n, k], {k, 0, n}]/2, {n, 0, 9}] (* James C. McMahon, Nov 03 2024 *)
PROG
(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
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Nov 02 2024
EXTENSIONS
a(9) from James C. McMahon, Nov 03 2024
STATUS
approved