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

%I A062144 #20 Sep 08 2022 08:45:03
%S A062144 1,54,1890,55440,1496880,38918880,998917920,25686460800,667847980800,
%T A062144 17660868825600,476843458291200,13178219210956800,373382877643776000,
%U A062144 10856825211488256000,324153781314435072000
%N A062144 Sixth (unsigned) column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).
%H A062144 Indranil Ghosh, <a href="/A062144/b062144.txt">Table of n, a(n) for n = 0..400</a>
%H A062144 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A062144 a(n) = (n+5)!*binomial(n+8, 8)/5!.
%F A062144 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.
%F A062144 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
%e A062144 a(2) = (2+5)! * binomial(2+8,8)/ 5! = (5040 * 45) / 120 = 1890. - _Indranil Ghosh_, Feb 24 2017
%t A062144 Table[(n+5)!*Binomial[n+8,8]/5!,{n,0,14}] (* _Indranil Ghosh_, Feb 24 2017 *)
%o A062144 (PARI) a(n)=(n+5)!*binomial(n+8, 8)/5! \\ _Indranil Ghosh_, Feb 24 2017
%o A062144 (Python)
%o A062144 import math
%o A062144 f=math.factorial
%o A062144 def C(n, r):return f(n)/f(r)/f(n-r)
%o A062144 def A062144(n): return f(n+5)*C(n+8, 8)/f(5) # _Indranil Ghosh_, Feb 24 2017
%o A062144 (Magma) [Factorial(n+5)*Binomial(n+8, 8)/Factorial(5): n in [0..20]]; // _G. C. Greubel_, May 11 2018
%Y A062144 Cf. A062143.
%K A062144 nonn,easy
%O A062144 0,2
%A A062144 _Wolfdieter Lang_, Jun 19 2001