A062152 - OEIS

A062152

Sixth (unsigned) column of triangle A062138 (generalized a=5 Laguerre).

1, 66, 2772, 96096, 3027024, 90810720, 2663781120, 77630192640, 2270683134720, 67111301537280, 2013339046118400, 61498356317798400, 1916698771904716800, 61039483966811750400, 1988143192061868441600

(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) = A062138(n+5, 5).

a(n) = (n+5)!*binomial(n+10, 10)/5!.

E.g.f.: N(5;5, x)/(1-x)^16 with N(5;5, x) := Sum_{k=0..5} A062190(5, k)* x^k = 1 + 50*x + 450*x^2 + 1200*x^3 + 1050*x^4 + 252*x^5.

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-10) = (-1)^n*f(n,10,-6), (n>=10). - Milan Janjic, Mar 01 2009

EXAMPLE

a(2) = (2+5)! * binomial(2+10,10) / 5! = (5040 * 66) / 120 = 2772. - Indranil Ghosh, Feb 24 2017

MATHEMATICA

Table[(n+5)!*Binomial[n+10, 10]/5!, {n, 0, 14}] (* Indranil Ghosh, Feb 24 2017 *)

PROG

(PARI) a(n) = (n+5)!*binomial(n+10, 10)/5! \\ Indranil Ghosh, Feb 24 2017

(Python)

import math

f=math.factorial

def C(n, r):return f(n)/f(r)/f(n-r)

def A062152(n): return f(n+5)*C(n+10, 10)/f(5) # Indranil Ghosh, Feb 24 2017

(Magma) [Factorial(n+5)*Binomial(n+10, 10)/Factorial(5): n in [0..20]]; // G. C. Greubel, May 11 2018