This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A376765 #21 Nov 03 2024 19:32:39
%S A376765 0,1,4,30,2308,9768755,1828549405062726,
%T A376765 378818692266223327546801733500,
%U A376765 822752278660977165496641302425735395827886114383655917217382408,1716153733051169540307898602341497569311487178262131715007420471535292324238528850823190109780802970900137357654221203141
%N A376765 a(n) = (1/2)*Sum_{k=0..n} n^binomial(n,k).
%C A376765 For n>0, this is one-half of (one possible definition of) the number of partial maps from an n-set to itself.
%t A376765 Table[Sum[n^Binomial[n,k],{k,0,n}]/2,{n,0,9}] (* _James C. McMahon_, Nov 03 2024 *)
%o A376765 (Python)
%o A376765 from math import comb
%o A376765 def A376765(n): return sum(n**comb(n,k) for k in range(n+1))>>1 # _Chai Wah Wu_, Nov 03 2024
%Y A376765 Cf. A000312, A007840, A376766.
%K A376765 nonn
%O A376765 0,3
%A A376765 _N. J. A. Sloane_, Nov 02 2024
%E A376765 a(9) from _James C. McMahon_, Nov 03 2024