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%I #17 Sep 08 2022 08:45:03
%S 1,32,720,14400,277200,5322240,103783680,2075673600,42810768000,
%T 913296384000,20183850086400,462393656524800,10981849342464000,
%U 270322445352960000,6893222356500480000,181981070211612672000
%N Fourth (unsigned) column sequence of triangle A062140 (generalized a=4 Laguerre).
%H Harry J. Smith, <a href="/A062261/b062261.txt">Table of n, a(n) for n=0..100</a>
%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F E.g.f.: (1+21*x+63*x^2+35*x^3)/(1-x)^11.
%F a(n) = A062140(n+3, 3).
%F a(n) = (n+3)!*binomial(n+7, 7)/3!.
%F 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
%t Table[(n+3)!*Binomial[n+7, 7]/3!, {n, 0, 30}] (* _G. C. Greubel_, May 13 2018 *)
%o (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
%o (Magma) [Factorial(n+3)*Binomial(n+7,7)/6: n in [0..30]]; // _G. C. Greubel_, May 13 2018
%Y Cf. A001720, A062199, A062260.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jun 19 2001
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