A062149 Third column sequence of triangle A062138 (generalized a=5 Laguerre).

1, 24, 432, 7200, 118800, 1995840, 34594560, 622702080, 11675664000, 228324096000, 4657811558400, 99084354969600, 2196369868492800, 50685458503680000, 1216451004088320000, 30330178368602112000

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Examples

			a(2) = (2+2)! * binomial(2+7,7) / 2! = (24 * 36) / 2 = 432. - _Indranil Ghosh_, Feb 24 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..400
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062148.

Programs

Magma

[Factorial(n+2)*Binomial(n+7,7)/2: n in [0..20]]; // G. C. Greubel, May 12 2018

Maple

a:=n-> (n+2)!*binomial(n+7, 7)/2!: seq(a(n), n=0..22); # Zerinvary Lajos, Apr 29 2007

Mathematica

Table[(n+2)!*Binomial[n+7,7]/2!,{n,0,15}] (* Indranil Ghosh, Feb 24 2017 *)

PARI

a(n)=(n+2)!*binomial(n+7, 7)/2! \\ Indranil Ghosh, Feb 24 2017

Python

import math
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
def A062149(n): return f(n+2)*C(n+7, 7)/f(2) # Indranil Ghosh, Feb 24 2017

Formula

E.g.f.: (1 + 14*x + 21*x^2)/(1 - x)^10.

a(n) = A062138(n+2, 2).

a(n) = (n+2)!*binomial(n+7, 7)/2!.

If we define f(n,i,x) = Sum_{k=i..n} Sum_{j=i..k} binomial(k,j) * Stirling1(n,k) * Stirling2(j,i) * x^(k-j), then a(n-2) = (-1)^n*f(n,2,-8), (n >= 2). - Milan Janjic, Mar 01 2009