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A062141 Third column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x). 4
1, 18, 252, 3360, 45360, 635040, 9313920, 143700480, 2335132800, 39956716800, 719220902400, 13599813427200, 269729632972800, 5602076992512000, 121645100408832000, 2757288942600192000, 65140951268929536000, 1601701037083090944000, 40932359836567879680000 (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+2)!*binomial(n+5, 5)/2!.

E.g.f.: (1 +10*x +10*x^2)/(1-x)^8.

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-5) = (-1)^(n-1)*f(n,5,-3), (n >= 5). - Milan Janjic, Mar 01 2009

EXAMPLE

a(2) = (2+2)! * binomial(2+5,5) / 2! = (24*21)/2 = 252. - Indranil Ghosh, Feb 24 2017

MAPLE

a:= n->(n+2)!*binomial(n+5, 5)/2!: seq(a(n), n=0..20); # Zerinvary Lajos, Apr 29 2007

MATHEMATICA

Table[(n+2)!*Binomial[n+5, 5]/2!, {n, 0, 15}] (* Indranil Ghosh, Feb 24 2017 *)

PROG

(Sage) [binomial(n, 5)*factorial (n-3)/2 for n in range(5, 21)] # Zerinvary Lajos, Jul 07 2009

(PARI) a(n)=(n+2)!*binomial(n+5, 5)/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 A062141(n): return f(n+2)*C(n+5, 5)/f(2) # Indranil Ghosh, Feb 24 2017

(PARI) x='x+O('x^30); Vec(serlaplace((1+10*x+10*x^2)/(1-x)^8)) \\ G. C. Greubel, May 11 2018

(MAGMA) [Factorial(n+2)*Binomial(n+5, 5)/2: n in [0..20]]; // G. C. Greubel, May 11 2018

CROSSREFS

Cf. A061206.

Sequence in context: A125475 A255371 A016175 * A157708 A159537 A136660

Adjacent sequences:  A062138 A062139 A062140 * A062142 A062143 A062144

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jun 19 2001

STATUS

approved

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Last modified June 5 03:12 EDT 2020. Contains 334828 sequences. (Running on oeis4.)