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A062150 Fourth (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre).

%I A062150 #18 Sep 08 2022 08:45:03
%S A062150 1,36,900,19800,415800,8648640,181621440,3891888000,85621536000,
%T A062150 1940754816000,45413662694400,1098184934246400,27454623356160000,
%U A062150 709596419051520000,18956361480376320000,523195576858386432000
%N A062150 Fourth (unsigned) column sequence of triangle A062138 (generalized a=5 Laguerre).
%H A062150 Indranil Ghosh, <a href="/A062150/b062150.txt">Table of n, a(n) for n = 0..400</a>
%H A062150 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A062150 E.g.f.: (1+24*x+84*x^2+56*x^3)/(1-x)^12.
%F A062150 a(n) = A062138(n+3, 3).
%F A062150 a(n) = (n+3)!*binomial(n+8, 8)/3!.
%F A062150 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,-9), (n>=3). - _Milan Janjic_, Mar 01 2009
%e A062150 a(2) = (2+3)! * binomial(2+8,8) / 3! = (120 * 45) / 6 = 900. - _Indranil Ghosh_, Feb 24 2017
%t A062150 Table[(n+3)!*Binomial[n+8,8]/3!,{n,0,15}] (* _Indranil Ghosh_, Feb 24 2017 *)
%o A062150 (PARI) a(n)=(n+3)!*binomial(n+8, 8)/3! \\ _Indranil Ghosh_, Feb 24 2017
%o A062150 (Python)
%o A062150 import math
%o A062150 f=math.factorial
%o A062150 def C(n, r):return f(n)/f(r)/f(n-r)
%o A062150 def A062150(n): return f(n+3)*C(n+8, 8)/f(3) # _Indranil Ghosh_, Feb 24 2017
%o A062150 (Magma) [Factorial(n+3)*Binomial(n+8, 8)/6: n in [0..20]]; // _G. C. Greubel_, May 12 2018
%Y A062150 Cf. A062149.
%K A062150 nonn,easy
%O A062150 0,2
%A A062150 _Wolfdieter Lang_, Jun 19 2001