A062142 Fourth (unsigned) column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

1, 28, 560, 10080, 176400, 3104640, 55883520, 1037836800, 19978358400, 399567168000, 8310997094400, 179819755315200, 4045944494592000, 94612855873536000, 2297740785500160000, 57903067794604032000

Offset

0,2

Links

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

Index entries for sequences related to Laguerre polynomials

Formula

a(n) = (n+3)!*binomial(n+6, 6)/3!; e.g.f.: (1 + 18*x + 45*x^2 + 20*x^3)/(1-x)^10.

If we define f(n,i,x) = Sum_{k=1..n} Sum_{j=1..k} binomial(k,j)*Stirling1(n,k)*Stirling2(j,i)*x^(k-j), then a(n-3) = (-1)^(n-1)*f(n,3,-7), (n>=3). - Milan Janjic, Mar 01 2009

Example

a(3) = (3+3)!*binomial(3+6,6)/3! = (720*84)/6 = 10080. - Indranil Ghosh, Feb 23 2017

Mathematica

Table[(n+3)!*Binomial[n+6, 6]/3!, {n, 0, 15}] (* Indranil Ghosh, Feb 23 2017 *)

Prog

(Sage) [binomial(n, 6)*factorial(n-3)/factorial(3) for n in range(6, 22)] # Zerinvary Lajos, Jul 07 2009
(PARI) a(n) =(n+3)!*binomial(n+6, 6)/3! \\ Indranil Ghosh, Feb 23 2017
(Python)
import math
f=math.factorial
def C(n, r):
    return f(n)/f(r)/f(n-r)
def A062142(n):return f(n+3)*C(n+6, 6)/f(3) # Indranil Ghosh, Feb 23 2017
(Magma) [Factorial(n+3)*Binomial(n+6, 6)/6: n in [0..20]]; // G. C. Greubel, May 12 2018

Crossrefs

Cf. A062137, A062141.

Sequence in context: A346322 A001234 A145149 * A240800 A281125 A234618

Adjacent sequences: A062139 A062140 A062141 * A062143 A062144 A062145

Keyword

nonn,easy

Author

Wolfdieter Lang, Jun 19 2001

Status

approved