A126804 a(n) = (2n)! / (n-1)!.

2, 24, 360, 6720, 151200, 3991680, 121080960, 4151347200, 158789030400, 6704425728000, 309744468633600, 15543540607795200, 841941782922240000, 48962152914554880000, 3042648073975910400000, 201220459292273541120000, 14110584707870682071040000

Offset

1,1

Comments

Old name was "Multiplying n X n integers above n".

a(n) = 2*A001814(n). - Zerinvary Lajos, May 03 2007

A179214(n) <= a(n). - Reinhard Zumkeller, Jul 05 2010

Product of the numbers from n to 2n. - Wesley Ivan Hurt, Dec 14 2015

Links

Robert Israel, Table of n, a(n) for n = 1..360

Elliot J. Carr and Matthew J. Simpson, Accurate and efficient calculation of finite response times for groundwater flow, arXiv:1707.06331 [physics.flu-dyn], 2017, p. 11.

Formula

a(n) = (2n)! / (n-1)!.

a(n) = Product_{i=n..2n} i. - Wesley Ivan Hurt, Dec 14 2015

From Robert Israel, Dec 15 2015: (Start)

a(n) = (2*n*(2*n-1)/(n-1))*a(n-1).

E.g.f.: 2*x/(1-4*x)^(3/2). (End)

a(n) = Pochhammer(n,n+1). - Pedro Caceres, Mar 10 2018

Example

a(5) = 151200 because five digits above 5: (6, 7, 8, 9, 10), multiplied by five equals 5*(6*7*8*9*10) = 151200.

Maple

a:=n->sum((count(Permutation(2*n+2), size=n+1)), j=0..n): seq(a(n), n=0..15); # Zerinvary Lajos, May 03 2007
seq(mul((n+k), k=0..n), n=1..16); # Zerinvary Lajos, Sep 21 2007
with(combstruct):with(combinat) :bin := {B=Union(Z, Prod(B, B))}: seq (count([B, bin, labeled], size=n)*(n-1), n=2..17); # Zerinvary Lajos, Dec 05 2007

Mathematica

Table[Pochhammer[n, n + 1], {n, 17}] (* Arkadiusz Wesolowski, Aug 13 2012 *)
Table[(2 n)!/(n - 1)!, {n, 20}] (* Wesley Ivan Hurt, Dec 14 2015 *)

Prog

(Magma) [Factorial(2*n)/Factorial(n-1) : n in [1..20]]; // Wesley Ivan Hurt, Dec 14 2015
(PARI) a(n) = prod(k=n, 2*n, k); \\ Michel Marcus, Dec 15 2015
(PARI) x='x+O('x^99); Vec(serlaplace(2*x/(1-4*x)^(3/2))) \\ Altug Alkan, Mar 11 2018

Crossrefs

Cf. A045943, A073838. - Reinhard Zumkeller, Jul 05 2010

Cf. A001814, A179214.

Sequence in context: A366003 A134805 A119702 * A344057 A170913 A090114

Adjacent sequences: A126801 A126802 A126803 * A126805 A126806 A126807

Keyword

easy,nonn

Author

Jonathan R. Love (japanada11(AT)yahoo.ca), Feb 22 2007

Extensions

New name from Wesley Ivan Hurt, Dec 15 2015

Status

approved