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A062151 Fifth column sequence of triangle A062138 (generalized a=5 Laguerre). 3

%I #20 Sep 08 2022 08:45:03

%S 1,50,1650,46200,1201200,30270240,756756000,19027008000,485188704000,

%T 12614906304000,335556507686400,9151541118720000,256243151324160000,

%U 7371918353479680000,217998157024327680000

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

%H Indranil Ghosh, <a href="/A062151/b062151.txt">Table of n, a(n) for n = 0..400</a>

%H <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>

%F E.g.f.: (1+36*x+216*x^2+336*x^3+126*x^4)/(1-x)^14.

%F a(n) = A062138(n+4, 4).

%F a(n) = (n+4)!*binomial(n+9, 9)/4!.

%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-9) = (-1)^(n-1)*f(n,9,-5), (n>=9). - _Milan Janjic_, Mar 01 2009

%e a(2) = (2+4)! * binomial(2+9,9) / 4! = (720 * 55)/ 24 = 1650. - _Indranil Ghosh_, Feb 24 2017

%t Table[(n+4)!*Binomial[n+9,9]/4!,{n,0,15}] (* _Indranil Ghosh_, Feb 24 2017 *)

%o (PARI) a(n) = (n+4)!*binomial(n+9,9)/4! \\ _Indranil Ghosh_, Feb 24 2017

%o (Python)

%o import math

%o f=math.factorial

%o def C(n, r):return f(n)/f(r)/f(n-r)

%o def A062151(n): return f(n+4)*C(n+9, 9)/f(4) # _Indranil Ghosh_, Feb 24 2017

%o (Magma) [Factorial(n+4)*Binomial(n+9,9)/Factorial(4): n in [0..20]]; // _G. C. Greubel_, May 12 2018

%Y Cf. A062150.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jun 19 2001

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Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)