cp's OEIS Frontend

A062149 Third column sequence of triangle A062138 (generalized a=5 Laguerre).

%I A062149 #28 Sep 08 2022 08:45:03
%S A062149 1,24,432,7200,118800,1995840,34594560,622702080,11675664000,
%T A062149 228324096000,4657811558400,99084354969600,2196369868492800,
%U A062149 50685458503680000,1216451004088320000,30330178368602112000
%N A062149 Third column sequence of triangle A062138 (generalized a=5 Laguerre).
%H A062149 Indranil Ghosh, <a href="/A062149/b062149.txt">Table of n, a(n) for n = 0..400</a>
%H A062149 <a href="/index/La#Laguerre">Index entries for sequences related to Laguerre polynomials</a>
%F A062149 E.g.f.: (1 + 14*x + 21*x^2)/(1 - x)^10.
%F A062149 a(n) = A062138(n+2, 2).
%F A062149 a(n) = (n+2)!*binomial(n+7, 7)/2!.
%F A062149 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-2) = (-1)^n*f(n,2,-8), (n >= 2). - _Milan Janjic_, Mar 01 2009
%e A062149 a(2) = (2+2)! * binomial(2+7,7) / 2! = (24 * 36) / 2 = 432. - _Indranil Ghosh_, Feb 24 2017
%p A062149 a:=n-> (n+2)!*binomial(n+7, 7)/2!: seq(a(n), n=0..22); # _Zerinvary Lajos_, Apr 29 2007
%t A062149 Table[(n+2)!*Binomial[n+7,7]/2!,{n,0,15}] (* _Indranil Ghosh_, Feb 24 2017 *)
%o A062149 (PARI)a(n)=(n+2)!*binomial(n+7, 7)/2! \\ _Indranil Ghosh_, Feb 24 2017
%o A062149 (Python)
%o A062149 import math
%o A062149 f=math.factorial
%o A062149 def C(n, r):return f(n)/f(r)/f(n-r)
%o A062149 def A062149(n): return f(n+2)*C(n+7, 7)/f(2) # _Indranil Ghosh_, Feb 24 2017
%o A062149 (Magma) [Factorial(n+2)*Binomial(n+7,7)/2: n in [0..20]]; // _G. C. Greubel_, May 12 2018
%Y A062149 Cf. A062148.
%K A062149 nonn,easy
%O A062149 0,2
%A A062149 _Wolfdieter Lang_, Jun 19 2001