A062261 Fourth (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).

1, 32, 720, 14400, 277200, 5322240, 103783680, 2075673600, 42810768000, 913296384000, 20183850086400, 462393656524800, 10981849342464000, 270322445352960000, 6893222356500480000, 181981070211612672000

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.

Programs

Magma

[Factorial(n+3)*Binomial(n+7,7)/6: n in [0..30]]; // G. C. Greubel, May 13 2018

Mathematica

Table[(n+3)!*Binomial[n+7, 7]/3!, {n, 0, 30}] (* G. C. Greubel, May 13 2018 *)

PARI

{ f=2; for (n=0, 100, f*=n + 3; write("b062261.txt", n, " ", f*binomial(n + 7, 7)/6) ) } \\ Harry J. Smith, Aug 03 2009

Formula

E.g.f.: (1+21*x+63*x^2+35*x^3)/(1-x)^11.

a(n) = A062140(n+3, 3).

a(n) = (n+3)!*binomial(n+7, 7)/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,-8), (n>=3). - Milan Janjic, Mar 01 2009