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A062152 Sixth (unsigned) column of triangle A062138 (generalized a=5 Laguerre).

%I A062152 #23 Aug 09 2022 02:29:11
%S A062152 1,66,2772,96096,3027024,90810720,2663781120,77630192640,
%T A062152 2270683134720,67111301537280,2013339046118400,61498356317798400,
%U A062152 1916698771904716800,61039483966811750400,1988143192061868441600
%N A062152 Sixth (unsigned) column of triangle A062138 (generalized a=5 Laguerre).
%H A062152 Indranil Ghosh, <a href="/A062152/b062152.txt">Table of n, a(n) for n = 0..400</a>
%H A062152 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A062152 a(n) = A062138(n+5, 5).
%F A062152 a(n) = (n+5)!*binomial(n+10, 10)/5!.
%F A062152 E.g.f.: N(5;5, x)/(1-x)^16 with N(5;5, x) := Sum_{k=0..5} A062190(5, k)* x^k = 1 + 50*x + 450*x^2 + 1200*x^3 + 1050*x^4 + 252*x^5.
%F A062152 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-10) = (-1)^n*f(n,10,-6), (n>=10). - _Milan Janjic_, Mar 01 2009
%e A062152 a(2) = (2+5)! * binomial(2+10,10) / 5! = (5040 * 66) / 120 = 2772. - _Indranil Ghosh_, Feb 24 2017
%t A062152 Table[(n+5)!*Binomial[n+10,10]/5!,{n,0,14}] (* _Indranil Ghosh_, Feb 24 2017 *)
%o A062152 (PARI) a(n) = (n+5)!*binomial(n+10,10)/5! \\ _Indranil Ghosh_, Feb 24 2017
%o A062152 (Python)
%o A062152 import math
%o A062152 f=math.factorial
%o A062152 def C(n, r):return f(n)/f(r)/f(n-r)
%o A062152 def A062152(n): return f(n+5)*C(n+10, 10)/f(5) # _Indranil Ghosh_, Feb 24 2017
%o A062152 (Magma) [Factorial(n+5)*Binomial(n+10,10)/Factorial(5): n in [0..20]]; // _G. C. Greubel_, May 11 2018
%Y A062152 Cf. A062138, A062151.
%K A062152 nonn,easy
%O A062152 0,2
%A A062152 _Wolfdieter Lang_, Jun 19 2001