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A062142 Fourth (unsigned) column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x). 2
1, 28, 560, 10080, 176400, 3104640, 55883520, 1037836800, 19978358400, 399567168000, 8310997094400, 179819755315200, 4045944494592000, 94612855873536000, 2297740785500160000, 57903067794604032000 (list; graph; refs; listen; history; text; internal format)
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(sum(binomial(k,j)*stirling1(n,k)*stirling2(j,i)*x^(k-j),j=i..k),k=i..n) 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. A062141.

Sequence in context: A278190 A001234 A145149 * A240800 A281125 A234618

Adjacent sequences:  A062139 A062140 A062141 * A062143 A062144 A062145

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

STATUS

approved

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Last modified February 25 11:54 EST 2020. Contains 332233 sequences. (Running on oeis4.)