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

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

Offset

0,3

Comments

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

Links

Table of n, a(n) for n=0..9.

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

Cf. A000312, A007840, A376766.

Sequence in context: A234566 A365366 A201974 * A221250 A119926 A103307

Adjacent sequences: A376762 A376763 A376764 * A376766 A376767 A376768

Keyword

nonn

Author

N. J. A. Sloane, Nov 02 2024

Extensions

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

Status

approved