A068605 Number of functions from [1,2,...,n] to [1,2,...,n] such that the image contains exactly two elements.

2, 18, 84, 300, 930, 2646, 7112, 18360, 45990, 112530, 270204, 638820, 1490762, 3440430, 7864080, 17825520, 40107726, 89652906, 199229060, 440401500, 968883762, 2122317318, 4630511064, 10066329000, 21810380150, 47110421826, 101468601612, 217969589460, 467077692570

Offset: 2

Author

Sharon Sela (sharonsela(AT)hotmail.com), Mar 29 2002

Keywords

• nonn
• easy

Comments

The sequence is the column corresponding to k=2 in A090657. - Geoffrey Critzer, Mar 06 2009

Links

• Stefano Spezia, Table of n, a(n) for n = 2..3200
• Index entries for linear recurrences with constant coefficients, signature (9,-33,63,-66,36,-8).

Crossrefs

Cf. A000918, A090657, A161680.

Programs

Mathematica

Table[ Binomial[n, 2]*(2^n - 2), {n, 2, 30}]

Python

def A068605(n): return n*(n-1)*((1<Chai Wah Wu, Jun 20 2025

Formula

a(n) = C(n, 2) * (2^n - 2).

O.g.f.: (4x^2/(1-2x)^3) - (2x^2/(1-x)^3). - Geoffrey Critzer, Mar 06 2009

E.g.f.: exp(x)*(2*exp(x) - 1)*x^2. - Stefano Spezia, May 06 2023

Extensions

Edited and extended by Robert G. Wilson v, Apr 17 2002