cp's OEIS Frontend

A062151 Fifth column sequence of triangle A062138 (generalized a=5 Laguerre).

%I A062151 #20 Sep 08 2022 08:45:03
%S A062151 1,50,1650,46200,1201200,30270240,756756000,19027008000,485188704000,
%T A062151 12614906304000,335556507686400,9151541118720000,256243151324160000,
%U A062151 7371918353479680000,217998157024327680000
%N A062151 Fifth column sequence of triangle A062138 (generalized a=5 Laguerre).
%H A062151 Indranil Ghosh, <a href="/A062151/b062151.txt">Table of n, a(n) for n = 0..400</a>
%H A062151 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A062151 E.g.f.: (1+36*x+216*x^2+336*x^3+126*x^4)/(1-x)^14.
%F A062151 a(n) = A062138(n+4, 4).
%F A062151 a(n) = (n+4)!*binomial(n+9, 9)/4!.
%F A062151 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-9) = (-1)^(n-1)*f(n,9,-5), (n>=9). - _Milan Janjic_, Mar 01 2009
%e A062151 a(2) = (2+4)! * binomial(2+9,9) / 4! = (720 * 55)/ 24 = 1650. - _Indranil Ghosh_, Feb 24 2017
%t A062151 Table[(n+4)!*Binomial[n+9,9]/4!,{n,0,15}] (* _Indranil Ghosh_, Feb 24 2017 *)
%o A062151 (PARI) a(n) = (n+4)!*binomial(n+9,9)/4! \\ _Indranil Ghosh_, Feb 24 2017
%o A062151 (Python)
%o A062151 import math
%o A062151 f=math.factorial
%o A062151 def C(n, r):return f(n)/f(r)/f(n-r)
%o A062151 def A062151(n): return f(n+4)*C(n+9, 9)/f(4) # _Indranil Ghosh_, Feb 24 2017
%o A062151 (Magma) [Factorial(n+4)*Binomial(n+9,9)/Factorial(4): n in [0..20]]; // _G. C. Greubel_, May 12 2018
%Y A062151 Cf. A062150.
%K A062151 nonn,easy
%O A062151 0,2
%A A062151 _Wolfdieter Lang_, Jun 19 2001