A062262 Fifth (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

1, 45, 1350, 34650, 831600, 19459440, 454053600, 10702692000, 256864608000, 6307453152000, 158947819430400, 4118193503424000, 109818493424640000, 3015784780968960000, 85303626661693440000

Offset: 0

Author

Wolfdieter Lang, Jun 19 2001

Keywords

• nonn
• easy

Links

• Harry J. Smith, Table of n, a(n) for n = 0..100
• Index entries for sequences related to Laguerre polynomials

Crossrefs

Cf. A001720, A062199, A062260, A062261.

Programs

Magma

[Factorial(n+4)*Binomial(n+8,8)/24: n in [0..30]]; // G. C. Greubel, May 13 2018

Mathematica

Table[(n+4)!*Binomial[n+8, 8]/4!, {n, 0, 30}] (* G. C. Greubel, May 13 2018 *)
With[{nn=20},CoefficientList[Series[(1+32x+168x^2+224x^3+70x^4)/(1-x)^13,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Mar 18 2025 *)

PARI

{ f=6; for (n=0, 100, f*=n + 4; write("b062262.txt", n, " ", f*binomial(n + 8, 8)/24) ) } \\ Harry J. Smith, Aug 03 2009

Formula

E.g.f.: (1+32*x+168*x^2+224*x^3+70*x^4)/(1-x)^13.

a(n) = A062140(n+4, 4).

a(n) = (n+4)!*binomial(n+8, 8)/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-4) = (-1)^n*f(n,4,-9), (n>=4). - Milan Janjic, Mar 01 2009