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

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

Offset

0,3

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

Links

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Main diagonal of A131182.

Cf. A336765.

Sequence in context: A061250 A183813 A222274 * A316998 A075387 A143857

Adjacent sequences: A061708 A061709 A061710 * A061712 A061713 A061714

Keyword

easy,nonn

Author

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

Status

approved