A062150 Fourth (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre).

1, 36, 900, 19800, 415800, 8648640, 181621440, 3891888000, 85621536000, 1940754816000, 45413662694400, 1098184934246400, 27454623356160000, 709596419051520000, 18956361480376320000, 523195576858386432000

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Examples

			a(2) = (2+3)! * binomial(2+8,8) / 3! = (120 * 45) / 6 = 900. - _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. A062149.

Programs

Magma

[Factorial(n+3)*Binomial(n+8, 8)/6: n in [0..20]]; // G. C. Greubel, May 12 2018

Mathematica

Table[(n+3)!*Binomial[n+8,8]/3!,{n,0,15}] (* Indranil Ghosh, Feb 24 2017 *)

PARI

a(n)=(n+3)!*binomial(n+8, 8)/3! \\ Indranil Ghosh, Feb 24 2017

Python

import math
f=math.factorial
def C(n, r):return f(n)/f(r)/f(n-r)
def A062150(n): return f(n+3)*C(n+8, 8)/f(3) # Indranil Ghosh, Feb 24 2017

Formula

E.g.f.: (1+24*x+84*x^2+56*x^3)/(1-x)^12.

a(n) = A062138(n+3, 3).

a(n) = (n+3)!*binomial(n+8, 8)/3!.

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-3)=(-1)^(n-1)*f(n,3,-9), (n>=3). - Milan Janjic, Mar 01 2009