A003308 a(n) = 2*n^(n-2).

2, 2, 6, 32, 250, 2592, 33614, 524288, 9565938, 200000000, 4715895382, 123834728448, 3584320788074, 113387824750592, 3892390136718750, 144115188075855872, 5724846103019631586, 242879062193188503552

Offset: 1

Author

Joseph Moser (jmoser(AT)wcupa.edu)

Keywords

• nonn

Comments

When n >=2, right side of binomial sum n-> Sum_{i=1..n-1} ( i^(n-i-1) * (n-i)^(i-1) *binomial(n, i) ). - Yong Kong (ykong(AT)curagen.com), Dec 28 2000

References

• A. P. Prudnikov, Yu. A. Brychkov and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992, Eq. (4.2.2.38)

Links

• G. C. Greubel, Table of n, a(n) for n = 1..250

Crossrefs

Cf. A000272.

Programs

Magma

[2*n^(n-2): n in [1..30]]; // G. C. Greubel, Jul 31 2022

Mathematica

Table[2*n^(n-2), {n,20}] (* Harvey P. Dale, Sep 18 2021 *)

SageMath

[2*n^(n-2) for n in (1..30)] # G. C. Greubel, Jul 31 2022

Formula

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

a(n) = 2 * A000272(n).

E.g.f.: (-2)*Integral_{t=0..x} LambertW(-t)/t dt = (-1)*LambertW(-x) * (LambertW(-x) + 2). - G. C. Greubel, Jul 31 2022