cp's OEIS Frontend

A062141 Third column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).

%I A062141 #28 Aug 09 2022 02:29:31
%S A062141 1,18,252,3360,45360,635040,9313920,143700480,2335132800,39956716800,
%T A062141 719220902400,13599813427200,269729632972800,5602076992512000,
%U A062141 121645100408832000,2757288942600192000,65140951268929536000,1601701037083090944000,40932359836567879680000
%N A062141 Third column sequence of coefficient triangle A062137 of generalized Laguerre polynomials n!*L(n,3,x).
%H A062141 Indranil Ghosh, <a href="/A062141/b062141.txt">Table of n, a(n) for n = 0..400</a>
%H A062141 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A062141 a(n) = (n+2)!*binomial(n+5, 5)/2!.
%F A062141 E.g.f.: (1 + 10*x + 10*x^2)/(1-x)^8.
%F A062141 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,-3), (n >= 5). - _Milan Janjic_, Mar 01 2009
%e A062141 a(2) = (2+2)! * binomial(2+5,5) / 2! = (24*21)/2 = 252. - _Indranil Ghosh_, Feb 24 2017
%p A062141 a:= n->(n+2)!*binomial(n+5, 5)/2!: seq(a(n), n=0..20); # _Zerinvary Lajos_, Apr 29 2007
%t A062141 Table[(n+2)!*Binomial[n+5,5]/2!,{n,0,15}] (* _Indranil Ghosh_, Feb 24 2017 *)
%o A062141 (Sage) [binomial(n,5)*factorial (n-3)/2 for n in range(5, 21)] # _Zerinvary Lajos_, Jul 07 2009
%o A062141 (PARI) a(n)=(n+2)!*binomial(n+5,5)/2! \\ _Indranil Ghosh_, Feb 24 2017
%o A062141 (Python)
%o A062141 import math
%o A062141 f=math.factorial
%o A062141 def C(n,r):return f(n)/f(r)/f(n-r)
%o A062141 def A062141(n): return f(n+2)*C(n+5,5)/f(2) # _Indranil Ghosh_, Feb 24 2017
%o A062141 (PARI) x='x+O('x^30); Vec(serlaplace((1+10*x+10*x^2)/(1-x)^8)) \\ _G. C. Greubel_, May 11 2018
%o A062141 (Magma) [Factorial(n+2)*Binomial(n+5,5)/2: n in [0..20]]; // _G. C. Greubel_, May 11 2018
%Y A062141 Cf. A061206, A062137.
%K A062141 nonn,easy
%O A062141 0,2
%A A062141 _Wolfdieter Lang_, Jun 19 2001