A061711 a(n) = n^n * n!.

1, 1, 8, 162, 6144, 375000, 33592320, 4150656720, 676457349120, 140587147048320, 36288000000000000, 11388728893445164800, 4270826380475341209600, 1886009588552176549862400, 968725766854884321342259200, 572622616354851562500000000000

Offset: 0

Author

Lorenzo Fortunato (fortunat(AT)pd.infn.it), Jun 19 2001

Keywords

• easy
• nonn

Comments

a(n) is the product of first n terms of an arithmetic progression with first term n and common difference n. E.g. a(3) = 3*6*9 = 162. - Amarnath Murthy, Sep 20 2003

Product of the entries in the last column of an n X n square array whose elements are the numbers 1..n^2 listed in increasing order by rows. - Wesley Ivan Hurt, Mar 31 2025

Examples

			a(1) = 1^1 * 1! = 1;
a(2) = 2^2 * 2! = 8;
a(3) = 3^3 * 3! = 162.
		

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100 (corrected by Michel Marcus, Jan 19 2019)

Crossrefs

Cf. A036679, A053042, A055775. - Vladimir Joseph Stephan Orlovsky, Jan 15 2009

Main diagonal of A131182.

Cf. A336765.

Programs

Magma

[Factorial(n)*n^n: n in [0..30]]; // G. C. Greubel, Nov 29 2022

Mathematica

Table[If[n == 0, 1, n^n] * n!, {n, 0, 20}] (* Vaclav Kotesovec, Mar 08 2018 *)

PARI

a(n) = n!*n^n; \\ Harry J. Smith, Jul 26 2009

Python

from math import factorial
def A061711(n): return factorial(n)*n**n # Chai Wah Wu, Sep 03 2022

Formula

E.g.f.: sinh(n*x)^n. - Vaclav Kotesovec, Nov 05 2014

a(n) = [x^n] 1/(1 - n*x/(1 - n*x/(1 - 2*n*x/(1 - 2*n*x/(1 - 3*n*x/(1 - 3*n*x/(1 - ...))))))), a continued fraction. - Ilya Gutkovskiy, Sep 20 2017

Sum_{n>=1} 1/a(n) = A336765. - Amiram Eldar, Nov 20 2020

a(n) ~ exp(-n)*n^(2*n)*sqrt(2*n*Pi). - Peter Luschny, Jan 10 2022