A062144 Sixth (unsigned) column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

1, 54, 1890, 55440, 1496880, 38918880, 998917920, 25686460800, 667847980800, 17660868825600, 476843458291200, 13178219210956800, 373382877643776000, 10856825211488256000, 324153781314435072000

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Examples

			a(2) = (2+5)! * binomial(2+8,8)/ 5! = (5040 * 45) / 120 = 1890. - _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. A062143.

Programs

Magma

[Factorial(n+5)*Binomial(n+8, 8)/Factorial(5): n in [0..20]]; // G. C. Greubel, May 11 2018

Mathematica

Table[(n+5)!*Binomial[n+8,8]/5!,{n,0,14}] (* Indranil Ghosh, Feb 24 2017 *)

PARI

a(n)=(n+5)!*binomial(n+8, 8)/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 A062144(n): return f(n+5)*C(n+8, 8)/f(5) # Indranil Ghosh, Feb 24 2017

Formula

a(n) = (n+5)!*binomial(n+8, 8)/5!.

E.g.f.: N(3;5, x)/(1-x)^14 with N(3;5, x) := Sum_{k=0..5} A062145(5, k) *x^k = 1 +40*x +280*x^2 +560*x^3 +350*x^4 +56*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-5) = (-1)^(n-1)*f(n,5, -9), (n>=5). - Milan Janjic, Mar 01 2009