A062151 Fifth column sequence of triangle A062138 (generalized a=5 Laguerre).

1, 50, 1650, 46200, 1201200, 30270240, 756756000, 19027008000, 485188704000, 12614906304000, 335556507686400, 9151541118720000, 256243151324160000, 7371918353479680000, 217998157024327680000

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Examples

			a(2) = (2+4)! * binomial(2+9,9) / 4! = (720 * 55)/ 24 = 1650. - _Indranil Ghosh_, Feb 24 2017
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..400
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A062150.

Programs

Magma

[Factorial(n+4)*Binomial(n+9,9)/Factorial(4): n in [0..20]]; // G. C. Greubel, May 12 2018

Mathematica

Table[(n+4)!*Binomial[n+9,9]/4!,{n,0,15}] (* Indranil Ghosh, Feb 24 2017 *)

PARI

a(n) = (n+4)!*binomial(n+9,9)/4! \\ Indranil Ghosh, Feb 24 2017

Python

import math
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
def A062151(n): return f(n+4)*C(n+9, 9)/f(4) # Indranil Ghosh, Feb 24 2017

Formula

E.g.f.: (1+36*x+216*x^2+336*x^3+126*x^4)/(1-x)^14.

a(n) = A062138(n+4, 4).

a(n) = (n+4)!*binomial(n+9, 9)/4!.

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-9) = (-1)^(n-1)*f(n,9,-5), (n>=9). - Milan Janjic, Mar 01 2009