A062143 Fifth column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

1, 40, 1080, 25200, 554400, 11975040, 259459200, 5708102400, 128432304000, 2968213248000, 70643475302400, 1733976211968000, 43927397369856000, 1148870392750080000, 31019500604252160000, 864410083505160192000

Offset

0,2

Comments

The coefficients of the numerator polynomials N(m,x) of the e.g.f. for column m (here m=4) give triangle A062145.

Links

Indranil Ghosh, Table of n, a(n) for n = 0..400

Index entries for sequences related to Laguerre polynomials

Formula

a(n) = (n+4)!*binomial(n+7, 7)/4!;

E.g.f.: (1 + 28*x + 126*x^2 + 140*x^3 + 35*x^4)/(1-x)^12.

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-4) = (-1)^n*f(n,4,-8), (n>=4). - Milan Janjic, Mar 01 2009

Example

a(3) = (3+4)! * binomial(3+7,7) / 4! = (5040 * 120) / 24 = 25200. - Indranil Ghosh, Feb 23 2017

Mathematica

Table[(n+4)!*Binomial[n+7, 7]/4!, {n, 0, 15}] (* Indranil Ghosh, Feb 23 2017 *)

Prog

(PARI) a(n) = (n+4)!*binomial(n+7, 7)/4! \\ Indranil Ghosh, Feb 23 2017
(Python)
import math
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
def A062143(n):return f(n+4)*C(n+7, 7)/f(4) # Indranil Ghosh, Feb 23 2017
(Magma) [Factorial(n+4)*Binomial(n+7, 7)/Factorial(4): n in [0..20]]; // G. C. Greubel, May 12 2018

Crossrefs

Cf. A062137, A062142, A062145.

Sequence in context: A028228 A165380 A075907 * A284838 A124100 A071952

Adjacent sequences: A062140 A062141 A062142 * A062144 A062145 A062146

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved